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A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Ali Saleh Alshomrani, Malik Zaka Ullah, Dumitru Baleanu
This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through
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Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Abdelhamid Mohammed Djaouti
We prove the global existence of small data solution in all spaces of all dimensions \(n\geq 1\) for weakly coupled systems of semilinear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, we assume that the nonlinearity terms \(f(t,u) \) and \(g(t,v) \) satisfy some properties of parabolic equations. We study the problem in several classes of regularity
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On nonlinear pantograph fractional differential equations with Atangana–Baleanu–Caputo derivative Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Mohammed S. Abdo, Thabet Abdeljawad, Kishor D. Kucche, Manar A. Alqudah, Saeed M. Ali, Mdi Begum Jeelani
In this paper, we obtain sufficient conditions for the existence and uniqueness results of the pantograph fractional differential equations (FDEs) with nonlocal conditions involving Atangana–Baleanu–Caputo (ABC) derivative operator with fractional orders. Our approach is based on the reduction of FDEs to fractional integral equations and on some fixed point theorems such as Banach’s contraction principle
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Dynamic behaviors of a nonautonomous predator–prey system with Holling type II schemes and a prey refuge Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Yumin Wu, Fengde Chen, Caifeng Du
In this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations
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Some new exact solutions of ( 3 + 1 ) $(3+1)$ -dimensional Burgers system via Lie symmetry analysis Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Elnaz Alimirzaluo, Mehdi Nadjafikhah, Jalil Manafian
In this paper, by using the Lie symmetry analysis, all of the geometric vector fields of the \((3+1)\)-Burgers system are obtained. We find the 1, 2, and 3-dimensional optimal system of the Burger system and then by applying the 3-dimensional optimal system reduce the order of the system. Also the nonclassical symmetries of the \((3+1)\)-Burgers system will be found by employing nonclassical methods
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Continuous stage stochastic Runge–Kutta methods Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Xuan Xin, Wendi Qin, Xiaohua Ding
In this work, a version of continuous stage stochastic Runge–Kutta (CSSRK) methods is developed for stochastic differential equations (SDEs). First, a general order theory of these methods is established by the theory of stochastic B-series and multicolored rooted tree. Then the proposed CSSRK methods are applied to three special kinds of SDEs and the corresponding order conditions are derived. In
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New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Muhammad Aamir Ali, Mujahid Abbas, Hüseyin Budak, Praveen Agarwal, Ghulam Murtaza, Yu-Ming Chu
In this research, we derive two generalized integral identities involving the \(q^{\varkappa _{2}}\)-quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the
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Modeling dynamics of fast food and obesity for evaluating the peer pressure effect and workout impact Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-21 Salma M. Al-Tuwairqi, Reem T. Matbouli
In recent years, chronic diseases, such as high blood pressure, diabetes, heart attack, and cancer, have increased around the world. Obesity is a common factor that makes individuals susceptible to these diseases. One reason for excessive weight gain is the frequent consumption of fast food. This study examined the impact that fast food has on obesity by analyzing the influence of peer pressure on
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Exponential stability for delayed complex-valued neural networks with reaction-diffusion terms Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-20 Xiaohui Xu, Jibin Yang, Quan Xu, Yanhai Xu, Shulei Sun
In this study, we investigate reaction-diffusion complex-valued neural networks with mixed delays. The mixed delays include both time-varying and infinite distributed delays. Criteria are derived to ensure the existence, uniqueness, and exponential stability of the equilibrium state of the addressed system on the basis of the M-matrix properties and homeomorphism mapping theories as well as the vector
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Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-20 Abdon Atangana, Seda İğret Araz
Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in
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Stability analysis of initial value problem of pantograph-type implicit fractional differential equations with impulsive conditions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-19 Arshad Ali, Ibrahim Mahariq, Kamal Shah, Thabet Abdeljawad, Bahaa Al-Sheikh
In this paper, we study an initial value problem for a class of impulsive implicit-type fractional differential equations (FDEs) with proportional delay terms. Schaefer’s fixed point theorem and Banach’s contraction principle are the key tools in obtaining the required results. We apply our results to a numerical problem for demonstration purpose.
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A fixed point approach to the solution of singular fractional differential equations with integral boundary conditions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-19 Kalaivani Chandran, Kalpana Gopalan, Sumaiya Tasneem Zubair, Thabet Abdeljawad
In this article, we first demonstrate a fixed point result under certain contraction in the setting of controlled b-Branciari metric type spaces. Thereafter, we specifically consider a following boundary value problem (BVP) for a singular fractional differential equation of order α: $$ \begin{aligned} &{}^{c}D^{\alpha }v(t) + h \bigl(t,v(t) \bigr) = 0,\quad 0< t< 1, \\ &v''(0) = v'''(0) = 0, \\ &v'(0)
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Dynamical analysis of a delayed food chain model with additive Allee effect Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-19 S. Vinoth, R. Sivasamy, K. Sathiyanathan, Grienggrai Rajchakit, P. Hammachukiattikul, R. Vadivel, Nallappan Gunasekaran
Dynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and it is assumed that there is a time lag due to the gestation effect in the intermediate predator. The interference among the prey and the intermediate predator is according to Holling type II
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Oscillation criteria for a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-19 Zhiyu Zhang, Ruihua Feng
In this paper, we study the oscillation of a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales. By using Riccati transformation and integral inequality, we establish several new theorems to ensure that each solution of the equation oscillates or asymptotically approaches zero, and the results in the literature are supplemented and extended. Examples
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Entire solutions for several second-order partial differential-difference equations of Fermat type with two complex variables Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-18 Hong Yan Xu, Da Wei Meng, Sanyang Liu, Hua Wang
This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type. By utilizing the Nevanlinna theory of meromorphic functions in several complex variables we obtain some results on the forms of entire solutions for these equations, which are some extensions and generalizations
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A new construction of Lupaş operators and its approximation properties Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-15 Mohd Qasim, Asif Khan, Zaheer Abbas, Qing-Bo Cai
The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences \(u_{m} \) and \(v_{m}\) of functions. We prove that the new operators provide better weighted uniform approximation over \([0,\infty )\). In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function
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Mixed nonlocal boundary value problem for implicit fractional integro-differential equations via ψ -Hilfer fractional derivative Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-14 Chatthai Thaiprayoon, Weerawat Sudsutad, Sotiris K. Ntouyas
In this paper, we investigate the existence and uniqueness of a solution for a class of ψ-Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, and Krasnosellskii’s fixed point theorems. Further, applying the techniques of nonlinear functional analysis, we establish various kinds of the Ulam stability results for the
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Modeling of pressure–volume controlled artificial respiration with local derivatives Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-14 Bahar Acay, Mustafa Inc, Yu-Ming Chu, Bandar Almohsen
We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung
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On zeros and growth of solutions of complex difference equations Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-13 Min-Feng Chen, Ning Cui
Let f be an entire function of finite order, let \(n\geq 1\), \(m\geq 1\), \(L(z,f)\not \equiv 0\) be a linear difference polynomial of f with small meromorphic coefficients, and \(P_{d}(z,f)\not \equiv 0\) be a difference polynomial in f of degree \(d\leq n-1\) with small meromorphic coefficients. We consider the growth and zeros of \(f^{n}(z)L^{m}(z,f)+P_{d}(z,f)\). And some counterexamples are given
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Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-12 Ruizhi Yang, Yuxin Ma, Chiyu Zhang
In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining
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Correction to: Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-12 Fatmawati, Muhammad Altaf Khan, Cicik Alfiniyah, Ebraheem Alzahrani
A Correction to this paper has been published: https://doi.org/10.1186/s13662-020-03199-3
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Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-12 Lanre Akinyemi, Mehmet Şenol, Shaheed N. Huseen
We propose a new modification of homotopy perturbation method (HPM) called the δ-homotopy perturbation transform method (δ-HPTM). This modification consists of the Laplace transform method, HPM, and a control parameter δ. This control convergence parameter δ in this new modification helps in adjusting and controlling the convergence region of the series solution and overcome some limitations of HPM
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Existence and Ulam–Hyers stability of a kind of fractional-order multiple point BVP involving noninstantaneous impulses and abstract bounded operator Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-11 Kaihong Zhao, Shoukai Deng
In this paper, we mainly study a kind of fractional-order multiple point boundary value problem involving noninstantaneous impulse and abstract bounded operator. The existence and uniqueness is obtained by the Banach contraction principle. And by applying direct analysis methods, we establish some conditions of the Ulam–Hyers stability for this problem. Finally, an interesting application example is
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An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-11 Ihteram Ali, Sirajul Haq, Kottakkaran Sooppy Nisar, Dumitru Baleanu
We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference method together with θ-weighted scheme. Then, for the approximation of spatial part of unknown function and its spatial derivatives, we use a mixed approach based on Lucas and Fibonacci polynomials
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Uniqueness of the Hadamard-type integral equations Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-09 Chenkuan Li
The goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko’s approach and Banach’s contraction principle. We also present several examples for illustration of the main theorems.
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Novel extended dissipativity criteria for generalized neural networks with interval discrete and distributed time-varying delays Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-09 Sunisa Luemsai, Thongchai Botmart, Wajaree Weera
The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapunov–Krasovskii functional (LKF), an improved Wirtinger single integral inequality, a novel triple integral inequality, and convex combination technique, the new asymptotic stability and extended
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Complexity analysis of cold chain transportation in a vaccine supply chain considering activity inspection and time-delay Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-09 Daoming Dai, Xuanyu Wu, Fengshan Si
The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-19 vaccines efficiently and safely to the areas affected by the epidemic. This paper focuses on vaccine transportation in a supply chain model composed of one distributor and one retailer (clinic
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Some extensions for the several combinatorial identities Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-09 Gao-Wen Xi, Qiu-Ming Luo
In this paper, we give some extensions for Mortenson’s identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving the harmonic numbers.
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Oscillation tests for first-order linear differential equations with non-monotone delays Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-09 Emad R. Attia
We study the oscillation of a first-order linear delay differential equation. A new technique is developed and used to obtain new oscillatory criteria for differential equation with non-monotone delay. Some of these results can improve many previous works. An example is introduced to illustrate the effectiveness and applicability of our results.
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Fundamental solutions for semidiscrete evolution equations via Banach algebras Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Jorge González-Camus, Carlos Lizama, Pedro J. Miana
We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic
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A study of a coupled system of Hadamard fractional differential equations with nonlocal coupled initial-multipoint conditions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Amjad F. Albideewi
In this paper, we obtain the existence results for a coupled system of Hadamard fractional differential equations supplemented with nonlocal coupled initial-multipoint conditions via fixed point theorems. An example is constructed for the illustration of the uniqueness result.
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Fuzzy stochastic differential equations driven by fractional Brownian motion Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Hossein Jafari, Marek T. Malinowski, M. J. Ebadi
In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions
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Hyers–Ulam stability of second-order differential equations using Mahgoub transform Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Antony Raj Aruldass, Divyakumari Pachaiyappan, Choonkil Park
The aim of this research is investigating the Hyers–Ulam stability of second-order differential equations. We introduce a new method of investigation for the stability of differential equations by using the Mahgoub transform. This is the first attempt of the investigation of Hyers–Ulam stability by using Mahgoub transform. We deal with both homogeneous and nonhomogeneous second-order differential equations
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On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Pavel Trojovský
Recently, Bednarz introduced a new two-parameter generalization of the Fibonacci sequence, which is called the \((k,p)\)-Fibonacci sequence and denoted by \((F_{k,p}(n))_{n\geq0}\). In this paper, we study the geometry of roots of the characteristic polynomial of this sequence.
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Robust stability analysis of impulsive quaternion-valued neural networks with distributed delays and parameter uncertainties Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Jielin Zhou, Yuanshun Tan, Xiaofeng Chen, Zijian Liu
In this paper, an impulsive quaternion-valued neural networks (QVNNs) model with leakage, discrete, and distributed delays is considered. Based on the homeomorphic mapping method, Lyapunov stability theorem, and linear matrix inequality (LMI) approach, sufficient conditions for the existence, uniqueness, and global robust stability of the equilibrium point of the impulsive QVNNs are provided. A numerical
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Dynamics of a class of host–parasitoid models with external stocking upon parasitoids Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Jasmin Bektešević, Vahidin Hadžiabdić, Senada Kalabušić, Midhat Mehuljić, Esmir Pilav
This paper is motivated by the series of research papers that consider parasitoids’ external input upon the host–parasitoid interactions. We explore a class of host–parasitoid models with variable release and constant release of parasitoids. We assume that the host population has a constant rate of increase, but we do not assume any density dependence regulation other than parasitism acting on the
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Dynamics analysis of an online gambling spreading model on scale-free networks Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Yu Kong, Tao Li, Yuanmei Wang, Xinming Cheng, He Wang, Yangmei Lei
Nowadays, online gambling has a great negative impact on the society. In order to study the effect of people’s psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new SHGD (susceptible–hesitator–gambler–disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive
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Some fractional Hermite–Hadamard-type inequalities for interval-valued coordinated functions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Fangfang Shi, Guoju Ye, Dafang Zhao, Wei Liu
The primary objective of this paper is establishing new Hermite–Hadamard-type inequalities for interval-valued coordinated functions via Riemann–Liouville-type fractional integrals. Moreover, we obtain some fractional Hermite–Hadamard-type inequalities for the product of two coordinated h-convex interval-valued functions. Our results generalize several well-known inequalities.
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Stable weak solutions to weighted Kirchhoff equations of Lane–Emden type Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Yunfeng Wei, Hongwei Yang, Hongwang Yu
This paper is concerned with the Liouville type theorem for stable weak solutions to the following weighted Kirchhoff equations: $$\begin{aligned}& -M \biggl( \int_{\mathbb{R}^{N}}\xi(z) \vert \nabla_{G}u \vert ^{2}\,dz \biggr){ \operatorname{div}}_{G} \bigl(\xi(z) \nabla_{G}u \bigr) \\& \quad=\eta(z) \vert u \vert ^{p-1}u,\quad z=(x,y) \in \mathbb{R}^{N}=\mathbb{R}^{N_{1}}\times\mathbb{R}^{N_{2}}
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Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Saeed Ahmad, Rafi Ullah, Dumitru Baleanu
This research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further
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The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Salih Djilali, Behzad Ghanbari
In this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate
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On fractional boundary value problems involving fractional derivatives with Mittag-Leffler kernel and nonlinear integral conditions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Mohammed S. Abdo, Thabet Abdeljawad, Saeed M. Ali, Kamal Shah
In this paper, we consider two classes of boundary value problems for nonlinear implicit differential equations with nonlinear integral conditions involving Atangana–Baleanu–Caputo fractional derivatives of orders \(0<\vartheta \leq 1\) and \(1<\vartheta \leq 2\). We structure the equivalent fractional integral equations of the proposed problems. Further, the existence and uniqueness theorems are proved
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Dynamical system of the growth of COVID-19 with controller Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Rabha W. Ibrahim, Dania Altulea, Rafida M. Elobaid
Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and
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The q -Sumudu transform and its certain properties in a generalized q -calculus theory Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Shrideh Khalaf Al-Omari
In this paper we consider a generalization to the q-calculus theory in the space of q-integrable functions. We introduce q-delta sequences and develop q-convolution products to derive certain q-convolution theorem. By using the concept of q-delta sequences, we establish various axioms and set up q-spaces of generalized functions named q-Boehmian spaces. The new assigned spaces of q-generalized functions
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A new efficient technique for solving modified Chua’s circuit model with a new fractional operator Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Manuel De la Sen, Sinan Deniz, Hasan Sözen
Chua’s circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua’s circuit is obtained by transforming the classical model of Chua’s circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua’s circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations
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Some k -fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Samaira Naz, Muhammad Nawaz Naeem, Yu-Ming Chu
In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several
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Qualitative properties of mathematical model of English language education Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Atena Ghasemabadi, Nahid Soltanian
This paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence
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Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Yuankui Ma, Dae San Kim, Hyunseok Lee, Hanyoung Kim, Taekyun Kim
The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind-type DC (Daehee and Changhee) sums and their generalizations
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Approximation of functions by a class of Durrmeyer–Stancu type operators which includes Euler’s beta function Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Abdullah Alotaibi, Faruk Özger, S. A. Mohiuddine, Mohammed A. Alghamdi
In this work, we construct the genuine Durrmeyer–Stancu type operators depending on parameter α in \([0,1]\) as well as \(\rho >0\) and study some useful basic properties of the operators. We also obtain Grüss–Voronovskaja and quantitative Voronovskaja types approximation theorems for the aforesaid operators. Further, we present numerical and geometrical approaches to illustrate the significance of
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Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-07 Adisorn Kittisopaporn, Pattrawut Chansangiam, Wicharn Lewkeeratiyutkul
We derive an iterative procedure for solving a generalized Sylvester matrix equation \(AXB+CXD = E\), where \(A,B,C,D,E\) are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the
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A fractional complex network model for novel corona virus in China Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-06 H. A. A. El-Saka, I. Obaya, H. N. Agiza
As is well known the novel coronavirus (COVID-19) is a zoonotic virus and our model is concerned with the effect of the zoonotic source of the coronavirus during the outbreak in China. We present a SEIS complex network epidemic model for the novel coronavirus. Our model is presented in fractional form and with varying population. The steady states and the basic reproductive number are calculated. We
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An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-06 Li-Bin Liu, Ying Liang, Xiaobing Bao, Honglin Fang
A system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval \([0,1]\). It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm
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Novel finite point approach for solving time-fractional convection-dominated diffusion equations Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-06 Xiaomin Liu, Muhammad Abbas, Honghong Yang, Xinqiang Qin, Tahir Nazir
In this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical
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Oscillation of nonlinear third-order difference equations with mixed neutral terms Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-05 Jehad Alzabut, Martin Bohner, Said R. Grace
In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify
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Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-04 Rubayyi T. Alqahtani
In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis
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Existence of chaos for partial difference equations via tangent and cotangent functions Adv. Differ. Equ. (IF 2.421) Pub Date : 2021-01-04 Haihong Guo, Wei Liang
This paper is concerned with the existence of chaos for a type of partial difference equations. We establish four chaotification schemes for partial difference equations with tangent and cotangent functions, in which the systems are shown to be chaotic in the sense of Li–Yorke or of both Li–Yorke and Devaney. For illustration, we provide three examples are provided.
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Simplified modelling and backstepping control of the long arm agricultural rover Adv. Differ. Equ. (IF 2.421) Pub Date : 2020-12-11 Napasool Wongvanich, Sungwan Boksuwan, Abdulhafiz Chesof
This paper presents the development of the simplified modelling and control of a long arm system for an agricultural rover, which also extends the modelling methodology from the previous work. The methodology initially assumes a flexible model and, through the use of the integral-based parameter identification method, the identified parameters are then correlated to an energy function to allow a construction
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Stabilization of nonlinear systems via aperiodic intermittent stochastic noise driven by G-Brownian motion with application to epidemic models Adv. Differ. Equ. (IF 2.421) Pub Date : 2020-12-11 Xiaojing Zhong, Feiqi Deng, Bo Zhang, Haibin Ouyang
To stabilize a nonlinear system \(dx(t)=f(t,x(t))\,dt\), we stochastically perturb the deterministic model by using two types of aperiodic intermittent stochastic noise driven by G-Brownian motion. We demonstrate quasi-sure exponential stability for the perturbed system and give the convergence rate, which is related to the control intensity. An application to SIS epidemic model is presented to confirm
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Lie symmetry reductions and conservation laws for fractional order coupled KdV system Adv. Differ. Equ. (IF 2.421) Pub Date : 2020-12-11 Hossein Jafari, Hong Guang Sun, Marzieh Azadi
Lie symmetry analysis is achieved on a new system of coupled KdV equations with fractional order, which arise in the analysis of several problems in theoretical physics and numerous scientific phenomena. We determine the reduced fractional ODE system corresponding to the governing factional PDE system. In addition, we develop the conservation laws for the system of fractional order coupled KdV equations
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Existence of local fractional integral equation via a measure of non-compactness with monotone property on Banach spaces Adv. Differ. Equ. (IF 2.421) Pub Date : 2020-12-10 Hemant Kumar Nashine, Rabha W. Ibrahim, Ravi P. Agarwal, N. H. Can
In this paper, we discuss fixed point theorems for a new χ-set contraction condition in partially ordered Banach spaces, whose positive cone \(\mathbb{K}\) is normal, and then proceed to prove some coupled fixed point theorems in partially ordered Banach spaces. We relax the conditions of a proper domain of an underlying operator for partially ordered Banach spaces. Furthermore, we discuss an application
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