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A family of interior-penalized weak Galerkin methods for second-order elliptic equations AIMS Math. (IF 0.882) Pub Date : 2020-10-19 Kaifang Liu; Lunji Song
Interior-penalized weak Galerkin (IPWG) finite element methods are proposed and analyzed for solving second order elliptic equations. The new methods employ the element $(\mathbb{P}_{k},\mathbb{P}_{k}, \mathcal{RT}_{k})$, with dimensions of space $d=2,3$, and the optimal a priori error estimates in discrete $H^1$-norm and $L^2$-norm are established. Moreover, provided enough smoothness of the exact
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Multi-valued versions of Nadler, Banach, Branciari and Reich fixed point theorems in double controlled metric type spaces with applications AIMS Math. (IF 0.882) Pub Date : 2020-10-19 Waseem Ahmad; Muhammad Sarwar; Thabet Abdeljawad; Gul Rahmat
In the current work, the multi-valued version of well-known theorems of Nadler, Banach, Branciari and Reich are generalized to the scope of double controlled metric space. A double controlled metric space is a metric type space in which the right hand side of the triangle inequality is controlled by two functions. Furthermore, applications to existence of solution to Volterra integral inclusions and
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A new generalized family of distributions: Properties and applications AIMS Math. (IF 0.882) Pub Date : 2020-10-19 Sajid Mehboob Zaidi; Mashail M. AL Sobhi; M. El-Morshedy; Ahmed Z. Afify
We come up with a new class called log-logistic tan generalized family which provides sub-models with left skewed, symmetrical, right skewed, unimodal, bimodal and reversed-J densities, and increasing, decreasing, modified bathtub, bathtub, unimodal, reversed-J shaped, and J-shaped hazard rates. Some of its sub-models are provided along with some general structural properties. The parameter estimation
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Blow up at well defined time for a coupled system of one spatial variable Emden-Fowler type in viscoelasticities with strong nonlinear sources AIMS Math. (IF 0.882) Pub Date : 2020-10-16 Fahima Hebhoub; Khaled Zennir; Tosiya Miyasita; Mohamed Biomy
For one spatial variable, a new kind of coupled system for nonlinear wave equations of Emden-Fowler type is considered with boundary value and initial values. Under certain conditions on the initial data and the exponent $\rho$, we show that the viscoelastic terms lead our problem to be dissipative and that the global solutions cannot exist in $L^2$ beyond the given finite time i.e., \[ \int_{r_1}^{r_2}
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Admissible multivalued hybrid $\mathcal{Z}$-contractions with applications AIMS Math. (IF 0.882) Pub Date : 2020-10-16 Monairah Alansari; Mohammed Shehu Shagari; Akbar Azam; Nawab Hussain
In this paper, we introduce new concepts, admissible multivalued hybrid $\mathcal{Z}$-contractions and multivalued hybrid $\mathcal{Z}$-contractions in the framework of $b$-metric spaces and establish sufficient conditions for existence of fixed points for such contractions. A few consequences of our main theorem involving linear and nonlinear contractions are pointed out and discussed by using variants
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A fractional Landweber iterative regularization method for stable analytic continuation AIMS Math. (IF 0.882) Pub Date : 2020-10-15 Fan Yang; Qianchao Wang; Xiaoxiao Li
In this paper, we consider the problem of analytic continuation of the analytic function $g(z)=g(x+iy)$ on a strip domain Ω=$\{z=x+iy\in \mathbb{C}|\,x\in\mathbb{R},0< y < y_0\}$, where the data is given only on the line $y=0$. This problem is a severely ill-posed problem. We propose the fraction Landweber iterative regularization method to deal with this problem. Under the a priori and a posteriori
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Geometric properties of a certain class of multivalent analytic functions associated with the second-order differential subordination AIMS Math. (IF 0.882) Pub Date : 2020-10-15 Yu-Qin Tao; Yi-Hui Xu; Rekha Srivastava; Jin-Lin Liu
We investigate some geometric properties of the class $\mathcal{Q}_n(A,B,\alpha)$ which is defined by the second-order differential subordination and find the sharp lower bound on $|z|=r<1$ for the following functional: $$\mathrm{Re}\left\{(1-\alpha)z^{1-p}f'(z) +\frac{\alpha}{p-1}z^{2-p}f''(z)\right\}$$ over the class $\mathcal{Q}_n(A,B,0)$.
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On distributional finite continuous Radon transform in certain spaces AIMS Math. (IF 0.882) Pub Date : 2020-10-14 Nitu Gupta; V. R. Lakshmi Gorty
The classical finite continuous Radon transform is extended to generalized functions on certain spaces. The inversion formula by the kernel method is shown in a weak distributional sense. In the concluding section, its application in Mathematical Physics is discussed.
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Study on weighted-based noniterative algorithms for centroid type-reduction of interval type-2 fuzzy logic systems AIMS Math. (IF 0.882) Pub Date : 2020-10-13 Yang Chen; Jinxia Wu; Jie Lan
Interval type-2 fuzzy logic systems (IT2 FLSs) have been widely used in many areas. Among which, type-reduction (TR) is an important block for theoretical study. Noniterative algorithms do not involve the complicated iteration process and obtain the system output directly. By discovering the inner relations between discrete and continuous noniterative algorithms, this paper proposes three types of
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Stability rate of a thermoelastic laminated beam: Case of equal-wave speed and nonequal-wave speed of propagation AIMS Math. (IF 0.882) Pub Date : 2020-10-12
In this article, we investigate a one-dimensional thermoelastic laminated beam system with viscoelastic dissipation on the effective rotation angle and through heat conduction in the interfacial slip equations. Under general conditions on the relaxation function and the relationship between the coefficients of the wave propagation speed of the first two equations, we show that the solution energy has
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Multidimensional stability of V-shaped traveling fronts in bistable reaction-diffusion equations with nonlinear convection AIMS Math. (IF 0.882) Pub Date : 2020-10-12 Hui-Ling Niu
This paper is concerned with the multidimensional stability of V-shaped traveling fronts for a reaction-diffusion equation with nonlinear convection term in $\mathbb{R}^n$ ($n\geq3$). We consider two cases for initial perturbations: one is that the initial perturbations decay at space infinity and another one is that the initial perturbations do not necessarily decay at space infinity. In the first
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Computing $\mu$-values for LTI Systems AIMS Math. (IF 0.882) Pub Date : 2020-10-12 Mutti-Ur Rehman; Jehad Alzabut; Javed Hussain Brohi
In this article we consider certain linear time-varying control systems and investigate their stability using structured singular values ($\mu$-values). We use the low rank ordinary differential equations based methodology to compute the lower bounds for $\mu$-values. The inner-outer algorithm computes the local extremizer of an admissible perturbation and adjusts the desired perturbation level. Further
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Necessary and sufficient conditions on the Schur convexity of a bivariate mean AIMS Math. (IF 0.882) Pub Date : 2020-10-10 Hong-Ping Yin; Xi-Min Liu; Jing-Yu Wang; Bai-Ni Guo
In the paper, the authors find and apply necessary and sufficient conditions for a bivariate mean of two positive numbers with three parameters to be Schur convex or Schur harmonically convex respectively.
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A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five AIMS Math. (IF 0.882) Pub Date : 2020-10-10 Raúl M. Falcón; Laura Johnson; Stephanie Perkins
This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of the Latin square and the cycle structure of the isotopism under consideration. Keeping then in mind that the autotopism group of a Latin square acts faithfully on the set of entries of
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An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration AIMS Math. (IF 0.882) Pub Date : 2020-10-10 Abdulkarim Hassan Ibrahim; Poom Kumam; Auwal Bala Abubakar; Umar Batsari Yusuf; Seifu Endris Yimer; Kazeem Olalekan Aremu
Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example
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Meromorphic harmonic univalent functions related with generalized (p,q)-post quantum calculus operators AIMS Math. (IF 0.882) Pub Date : 2020-12-09 Shuhai Li; Lina Ma; Huo Tang
In this paper, we introduce certain subclasses of meromorphic harmonic univalent functions, which are defined by using generalized (p, q)-post quantum calculus operators as well as subordination relationship. Sufficient coefficient conditions, extreme points, distortion bounds and convolution properties for functions belonging to the subclasses are obtained.
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The existence of a compact global attractor for a class of competition model AIMS Math. (IF 0.882) Pub Date : 2020-10-09 Yanxia Wu
This paper is concerned with the existence of a compact global attractor for a class of competition model in n−dimensional (n ≥ 1) domains. Using mathematical induction and more detailed interpolation estimates, especially Gagliardo-Nirenberg inequality, we obtain the existence of a compact global attractor, which implies the uniform boundedness of the global solutions. In particular, we get that the
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Study of mathematical model of Hepatitis B under Caputo-Fabrizo derivative AIMS Math. (IF 0.882) Pub Date : 2020-10-09 Sajjad Ali Khan; Kamal Shah; Poom Kumam; Aly Seadawy; Gul Zaman; Zahir Shah
The current work is devoted to bring out a detail analysis including qualitative and semi-analytical study of Hepatitis B model under the Caputo- Fabrizio fractional derivative (CFFD). For the required results, fixed point theory is used to establish the conditions for existence and uniqueness of solution to the considered model. On the other hand, for semi analytical solutions, we use decomposition
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On the extinction of continuous-state branching processes in random environments AIMS Math. (IF 0.882) Pub Date : 2020-10-09 Xiangqi Zheng
This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Lévy random environments. Some results on extinction are presented, including the distribution of the extinction time, the limiting distribution conditioned on large extinction times and the asymptotic behavior near extinction. This paper also provides a new time-space transformation which
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Existence and Hyers-Ulam type stability results for nonlinear coupled system of Caputo-Hadamard type fractional differential equations AIMS Math. (IF 0.882) Pub Date : 2020-10-09 Subramanian Muthaiah; Dumitru Baleanu; Nandha Gopal Thangaraj
This paper aims to present the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions. The fractional derivative of the Caputo-Hadamard type is used to formulate the FDEs, and the fractional integrals described in the boundary conditions are due to Hadamard. The consequence
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On the nonstandard numerical discretization of SIR epidemic model with a saturated incidence rate and vaccination AIMS Math. (IF 0.882) Pub Date : 2020-09-30 Agus Suryanto; Isnani Darti
Recently, Hoang and Egbelowo (Boletin de la Sociedad Matemàtica Mexicana, 2020) proposed a nonstandard finite difference scheme (NSFD) to get a discrete SIR epidemic model with saturated incidence rate and constant vaccination. The discrete model was derived by discretizing the right-hand sides of the system locally and the first order derivative is approximated by the generalized forward difference
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Stability of general pathogen dynamic models with two types of infectious transmission with immune impairment AIMS Math. (IF 0.882) Pub Date : 2020-09-30 B. S. Alofi; S. A. Azoz
In this paper, we investigate the global properties of two general models of pathogen infection with immune deficiency. Both pathogen-to-cell and cell-to-cell transmissions are considered. Latently infected cells are included in the second model. We show that the solutions are nonnegative and bounded. Lyapunov functions are organized to prove the global asymptotic stability for uninfected and infected
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Exponential stability analysis and control design for nonlinear system with time-varying delay AIMS Math. (IF 0.882) Pub Date : 2020-09-29 Xuelian Jin
This paper investigates the problem of exponential stability analysis and control design for time delay nonlinear systems with unknown control coefficient. Nussbaum gain function is utilized to solve the problem of unknown control directions at every step. By designing a new Lyapunov-Krasovskii functional, the problem of unknown time-varying delay is solved. Under the frame of adaptive backstepping
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Tikhonov-type regularization method for a sideways problem of the time-fractional diffusion equation AIMS Math. (IF 0.882) Pub Date : 2020-09-29 Hongwu Zhang; Xiaoju Zhang
A sideways problem of the time-fractional diffusion equation is investigated. The solution of this problem does not depend on the given data. In view of this, this article uses a Tikhonov-type regularized method to construct an approximate solution and overcome the ill-posedness of considered problem. The a-posteriori convergence estimates of logarithmic and double logarithmic types for the regularized
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On geometry of isophote curves in Galilean space AIMS Math. (IF 0.882) Pub Date : 2020-09-28 Zühal Küçükarslan Yüzbaşı; Dae Won Yoon
In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an isotropic or a non-isotropic vector. We also give a method to compute isophote curves of surfaces of revolution. Subsequently, we show the relationship between isophote
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Some (p, q)-Hardy type inequalities for (p, q)-integrable functions AIMS Math. (IF 0.882) Pub Date : 2020-09-28 Suriyakamol Thongjob; Kamsing Nonlaopon; Sortiris K. Ntouyas
In this paper, we study some $(p,q)$-Hardy type inequalities for $(p,q)$-integrable functions. Moreover, we also study $(p,q)$-Hölder integral inequality and $(p,q)$-Minkowski integral inequality for two variables. By taking $p=1$ and $q\to 1$, our results reduce to classical results on Hardy type inequalities, Hölder integral inequality and Minkowski integral inequality for two variables.
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Weak and pseudo-solutions of an arbitrary (fractional) orders differential equation in nonreflexive Banach space AIMS Math. (IF 0.882) Pub Date : 2020-09-28 H. H. G. Hashem; A. M. A. El-Sayed; Maha A. Alenizi
In this paper, we establish some existence results of weak solutions and pseudo-solutions for the initial value problem of the arbitrary (fractional) orders differential equation \[ %\frac{dx}{dt}~=~ f(t,D^\gamma x(t)),~\gamma \in (0,1), ~~t~\in~I=[0,T] %\] \begin{eqnarray*}\label{2} \hspace{-3cm}\frac{dx}{dt}&=& f(t,D^\gamma x(t)),~\gamma \in (0,1), ~~t~\in~[0,T]=\mathbb{I}\nonumber\\ &&\\ x(0)&=&x_0
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An averaging principle for stochastic evolution equations with jumps and random time delays AIMS Math. (IF 0.882) Pub Date : 2020-09-28 Min Han; Bin Pei
This paper investigates an averaging principle for stochastic evolution equations with jumps and random time delays modulated by two-time-scale Markov switching processes in which both fast and slow components co-exist. We prove that there exists a limit process (averaged equation) being substantially simpler than that of the original one.
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Hermite-Hadamard inequality for new generalized conformable fractional operators AIMS Math. (IF 0.882) Pub Date : 2020-09-28 Tahir Ullah Khan; Muhammad Adil Khan
This paper is concerned to establish an advanced form of the well-known Hermite-Hadamard (HH) inequality for recently-defined Generalized Conformable (GC) fractional operators. This form of the HH inequality combines various versions (new and old) of this inequality, containing operators of the types Katugampula, Hadamard, Riemann-Liouville, conformable and Riemann, into a single form. Moreover, a
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A delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response AIMS Math. (IF 0.882) Pub Date : 2020-09-28 Yougang Wang; Anwar Zeb; Ranjit Kumar Upadhyay; A Pratap
This paper gropes the stability and Hopf bifurcation of a delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response. The critical point at which a Hopf bifurcation occurs can be figured out by using the escalating time delay of psychologically addicts as a bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are explored
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New results on complex conformable integral AIMS Math. (IF 0.882) Pub Date : 2020-09-27 Francisco Martínez; Inmaculada Martínez; Mohammed K. A. Kaabar; Silvestre Paredes
A new theory of analytic functions has been recently introduced in the sense of conformable fractional derivative. In addition, the concept of fractional contour integral has also been developed. In this paper, we propose and prove some new results on complex fractional integration. First, we establish necessary and sufficient conditions for a continuous function to have antiderivative in the conformable
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Ruled surfaces with constant Disteli-axis AIMS Math. (IF 0.882) Pub Date : 2020-09-27 Nadia Alluhaibi
This work develops the kinematic-geometry for ruled surfaces by using the analogy with spherical kinematics. This provides the ability to compute set of curvature functions which define the local shape of ruled surfaces. Hence, the well known equation of the Plücker’s conoid has been obtained and its kinematic-geometry are examined in details. Finally, a characterization for a line trajectory to be
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A stochastic epidemic model of COVID-19 disease AIMS Math. (IF 0.882) Pub Date : 2020-09-26 Xavier Bardina; Marco Ferrante; Carles Rovira
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases.
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Is the Allee effect relevant in cancer evolution and therapy? AIMS Math. (IF 0.882) Pub Date : 2020-09-25 Marcello Delitala; Mario Ferraro
Most models of cancer assume that tumor cells populations, at low densities, grow exponentially to be eventually limited by the available amount of resources such as space and nutrients. However, recent pre-clinical and clinical data of cancer onset or recurrence indicate the presence of a population dynamics in which growth rates increase with cell numbers. Such effect is analogous to the cooperative
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On an integral and consequent fractional integral operators via generalized convexity AIMS Math. (IF 0.882) Pub Date : 2020-09-25 Wenfeng He; Ghulam Farid; Kahkashan Mahreen; Moquddsa Zahra; Nana Chen
Fractional calculus operators are very useful in basic sciences and engineering. In this paper we study an integral operator which is directly related with many known fractional integral operators. A new generalized convexity namely exponentially (α, h−m)-convexity is defined which has been applied to obtain the bounds of unified integral operators. A generalized Hadamard inequality is established
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On graded 2-absorbing $I_{e}$-prime submodules of graded modules over graded commutative rings AIMS Math. (IF 0.882) Pub Date : 2020-09-25 Shatha Alghueiri; Khaldoun Al-Zoubi
Let $G$ be an abelian group with identity $e$. Let $R$ be a $G$-graded commutative ring with identity and $M$ a graded $R$-module. In this paper, we introduce the concept of graded 2-absorbing $I_{e}$-prime submodule as a generalization of a graded 2-absorbing prime submodule for $\ I=\oplus _{g\in G}I_{g}$ a fixed graded ideal of $R$. We give a number of results concerning these classes of graded
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Efficient estimation combining exponential and ln functions under two phase sampling AIMS Math. (IF 0.882) Pub Date : 2020-09-24 Yasir Hassan; Muhammad Ismail; Will Murray; Muhammad Qaiser Shahbaz
In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study
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The inequalities for the analysis of a class of ternary refinement schemes AIMS Math. (IF 0.882) Pub Date : 2020-09-24 Ghulam Mustafa; Syeda Tehmina Ejaz; Dumitru Baleanu; Yu-Ming Chu
The ternary refinement schemes are the generalized version of the binary refinement schemes. This class of the schemes produce the smooth curves with the less number of refinement steps as compared to the binary class of schemes. In this paper, we present the inequalities for the analysis of a class of ternary refinement schemes. There are three simple algebraic expressions in each inequality. Further
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On Reidemeister torsion of flag manifolds of compact semisimple Lie groups AIMS Math. (IF 0.882) Pub Date : 2020-09-24 Cenap Özel; Habib Basbaydar; Yasar Sözen; Erol Yilmaz; Jung Rye Lee; Choonkil Park
In this paper we calculate Reidemeister torsion of flag manifold $K/T$ of compact semi-simple Lie group $K=SU_{n+1}$ using Reidemeister torsion formula and Schubert calculus, where $T$ is maximal torus of $K$. We find that this number is 1. Also we explicitly calculate ring structure of integral cohomology algebra of flag manifold $K/T$ of compact semi-simple Lie group $K=SU_{n+1 }$ using root data
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Mathematical study of SIR epidemic model under convex incidence rate AIMS Math. (IF 0.882) Pub Date : 2020-09-24 Rahim ud Din; Kamal Shah; Manar A. Alqudah; Thabet Abdeljawad; Fahd Jarad
In this manuscript, we examine the SIR model under convex incidence rate. We first formulate the famous SIR model under the aforesaid incidence rate. Further, we develop some sufficient analysis to examine the dynamical behavior of the model under consideration. We compute the basic reproductive number $\mathcal{R}_0.$ Also we study the global attractivity results via using Dulac function theory. Further
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Integral transforms of an extended generalized multi-index Bessel function AIMS Math. (IF 0.882) Pub Date : 2020-09-24 Shahid Mubeen; Rana Safdar Ali; Iqra Nayab; Gauhar Rahman; Thabet Abdeljawad; Kottakkaran Sooppy Nisar
In this paper, we discuss the extended generalized multi-index Bessel function by using the extended beta type function. Then we investigate its several properties including integral representation, derivatives, beta transform, Laplace transform, Mellin transforms, and some relations of extension of extended generalized multi-index Bessel function (E1GMBF) with the Laguerre polynomial and Whittaker
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Periodic boundary value problem involving sequential fractional derivatives in Banach space AIMS Math. (IF 0.882) Pub Date : 2020-09-23 Xinwei Su; Shuqin Zhang; Lixin Zhang
In this paper, by the method of upper and lower solutions coupled with the monotone iterative technique, we investigate the existence and uniqueness results of solutions for a periodic boundary value problem of nonlinear fractional differential equation involving conformable sequential fractional derivatives in Banach space. An example is given to illustrate our main result.
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A certain two-term exponential sum and its fourth power means AIMS Math. (IF 0.882) Pub Date : 2020-09-23 Zhang Jin; Zhang Wenpeng
The main purpose of this article is using the properties of the Legendre’s symbol and the classical Gauss sums to study the calculating problem of the fourth power mean of a certain two-term exponential sums, and give an interesting calculating formula for it.
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A 3D proposal for the visualization of speed in railway networks AIMS Math. (IF 0.882) Pub Date : 2020-09-22 Alberto Almech; Eugenio Roanes-Lozano
This article deals with a proposal for visualizing the speed of the different sections of the lines of a railway network that has been implemented in the computer algebra system Maple. The idea is to organize the data (the speed in the different sections of the railway network) as a weighted graph. The endpoints of the sections considered are the vertices of the graph and the edges are the sections
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On pursuit-evasion differential game problem in a Hilbert space AIMS Math. (IF 0.882) Pub Date : 2020-09-22 Jamilu Adamu; Kanikar Muangchoo; Abbas Ja’afaru Badakaya; Jewaidu Rilwan
We consider a pursuit-evasion differential game problem in which countably many pursuers chase one evader in the Hilbert space ${\ell_2}$ and for a fixed period of time. Dynamic of each of the pursuer is governed by first order differential equations and that of the evader by a second order differential equation. The control function for each of the player satisfies an integral constraint. The distance
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A Fuglede-Putnam property for N-class A(k) operators AIMS Math. (IF 0.882) Pub Date : 2020-09-22 Ahmed Bachir; Durairaj Senthilkumar; Nawal Ali Sayyaf
This paper studies the Fuglede-Putnam's property for $N$-class $A(k)$ operators and $\mathcal{Y}$ class operators. Some range-kernel orthogonality results of the generalized derivation induced by the above classes of operators are given.
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Uniqueness of meromorphic functions sharing small functions in the k-punctured complex plane AIMS Math. (IF 0.882) Pub Date : 2020-09-21 Xian Min Gui; Hong Yan Xu; Hua Wang
The main purpose of this article is concerned with the uniqueness of meromorphic functions in the $k$-punctured complex plane $\Omega$ sharing five small functions with finite weights. We proved that for any two admissible meromorphic functions $f$ and $g$ in $\Omega$, if $\widetilde{E}_\Omega(\alpha_j,l;f)=\widetilde{E}_\Omega(\alpha_j,l; g)$ and an integer $l\geq 22$, then $f\equiv g$, where $\alpha_j~(j=1
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Long-time asymptotics for the generalized Sasa-Satsuma equation AIMS Math. (IF 0.882) Pub Date : 2020-09-21 Kedong Wang; Xianguo Geng; Mingming Chen; Ruomeng Li
In this paper, we study the long-time asymptotic behavior of the solution of the Cauchy problem for the generalized Sasa-Satsuma equation. Starting with the 3 × 3 Lax pair related to the generalized Sasa-Satsuma equation, we construct a Rieman-Hilbert problem, by which the solution of the generalized Sasa-Satsuma equation is converted into the solution of the corresponding RiemanHilbert problem. Using
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A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation AIMS Math. (IF 0.882) Pub Date : 2020-09-21 Muammer Ayata; Özan Ozkan
In this study, it is the first time that conformable Laplace decomposition method (CLDM) is applied to fractional Newell-Whitehead-Segel (NWS) equation which is one of the most significant amplitude equations in physics. The method consists of the unification of conformable Laplace transform and Adomian decomposition method (ADM) and it is used for finding approximate analytical solutions of linear-nonlinear
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Novel stability criteria on a patch structure Nicholson’s blowflies model with multiple pairs of time-varying delays AIMS Math. (IF 0.882) Pub Date : 2020-09-21 Xin Long
This paper investigates a patch structure Nicholson’s blowflies model involving multiple pairs of different time-varying delays. Without assuming the uniform positiveness of the death rate and the boundedness of coefficients, we establish three novel criteria to check the global convergence, generalized exponential convergence and asymptotical stability on the zero equilibrium point of the addressed
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Positive periodic solution of first-order neutral differential equation with infinite distributed delay and applications AIMS Math. (IF 0.882) Pub Date : 2020-09-18 Zhibo Cheng; Lisha Lv; Jie Liu
In this paper, we consider first-order neutral differential equation with infinite distributed delay, where nonlinear term may satisfy sub-linearity, semi-linearity and super-linearity conditions. By virtue of a fixed point theorem of Leray-Schauder type, we prove the existence of positive periodic solutions. As applications, we prove that Hematopoiesis model, Nicholson’s blowflies model and the model
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Properties of positive solutions for a fractional boundary value problem involving fractional derivative with respect to another function AIMS Math. (IF 0.882) Pub Date : 2020-09-18 Yitao Yang; Dehong Ji
In this article, we develop the existence and uniqueness of positive solutions to a class of fractional boundary value problems involving fractional order derivative with respect to another function for any given parameter. The analysis is based upon the fixed point theorems of concave operators in partial ordering Banach spaces. For the sake of discussing the existence of solutions for the problem
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Locally finiteness and convolution products in groupoids AIMS Math. (IF 0.882) Pub Date : 2020-09-18 In Ho Hwang; Hee Sik Kim; Joseph Neggers
In this paper, we introduce a version of the Moebius function and other special functions on a particular class of intervals for groupoids, and study them to obtain results analogous to those obtained in the usual lattice, combinatorics and number theory setting, but of course much more general due to the viewpoint taken in this paper.
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Refinement and corrigendum of bounds of fractional integral operators containing Mittag-Leffler functions AIMS Math. (IF 0.882) Pub Date : 2020-09-18 Ghulam Farid; Maja Andrić; Maryam Saddiqa; Josip Pečarić; Chahn Yong Jung
The main objective of this paper is to compute refinements of bounds of the generalized fractional integral operators containing an extended generalized Mittag-Leffler function in their kernels. The presented results also provide refinements of already known bounds of different fractional integral operators for convex, m-convex, s-convex and (s, m)-convex functions. Moreover, the refinements of some
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Integral inequalities of Hermite-Hadamard type for quasi-convex functions with applications AIMS Math. (IF 0.882) Pub Date : 2020-09-18 Pshtiwan Othman Mohammed; Miguel Vivas-Cortez; Thabet Abdeljawad; Yenny Rangel-Oliveros
There is a strong connection between convexity and inequalities. So, techniques from each concept applies to the other due to the strong correlation between them; specifically, in the past few years. In this attempt, we consider the Hermite–Hadamard inequality and related inequalities for the class of functions whose absolute value of the third derivative are quasi-convex functions. Finally, the applications
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On Uzawa-SSI method for non-Hermitian saddle point problems AIMS Math. (IF 0.882) Pub Date : 2020-09-18 Shu-Xin Miao; Jing Zhang
Based on the single-step iteration (SSI) method for the non-Hermitian positive definite linear systems, we propose a Uzawa-SSI method for solving the saddle point problems with non-Hermitian positive definite (1, 1) block in this paper. The convergence and semi-convergence properties of the Uzawa-SSI method, respectively, for nonsingular and singular cases are analyzed. Numerical examples with experiments
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Properties of the power-mean and their applications AIMS Math. (IF 0.882) Pub Date : 2020-09-17 Jing-Feng Tian; Ming-Hu Ha; Hong-Jie Xing
Suppose $w,v>0$, $w\neq v$ and $A_{u}\left (w,v\right) $ is the $u$-order power mean (PM) of $w$ and $v$. In this paper, we completely describe the convexity of $u\mapsto A_{u}\left (w,v\right) $ on $\mathbb{R}$ and $% s\mapsto A_{u\left (s\right) }\left (w,v\right) $ with $u\left (s\right) =\left (\ln 2\right) /\ln \left (1/s\right) $ on $\left (0,\infty \right) $. These yield some new inequalities
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Explicit solutions to the Sharma-Tasso-Olver equation AIMS Math. (IF 0.882) Pub Date : 2020-09-17 Mohammed Aly Abdou; Loubna Ouahid; Saud Owyed; A. M. Abdel-Baset; Mustafa Inc; Mehmet Ali Akinlar; Yu-Ming Chu
We present new exact traveling wave solutions of generalized Sharma-Tasso-Olver (STO) with variable coefficients using three different methods, namely the extended F-expansion, the new sub-equations, and generalized Kudryashov expansion. We obtain new solutions with the form of solitons, triangular and rational functions. Computational results indicate that these methods are very useful and easily
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A certain subclass of bi-univalent functions associated with Bell numbers and $q-$Srivastava Attiya operator AIMS Math. (IF 0.882) Pub Date : 2020-09-17 Erhan Deniz; Muhammet Kamali; Semra Korkmaz
In the present study, we introduced general a subclass of bi-univalent functions by using the Bell numbers and $q-$Srivastava Attiya operator. Also, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.
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Derivation of logarithmic integrals expressed in teams of the Hurwitz zeta function AIMS Math. (IF 0.882) Pub Date : 2020-09-16 Robert Reynolds; Allan Stauffer
In this paper by means of contour integration we will evaluate definite integrals of the form \begin{equation*} \int_{0}^{1}\left(\ln^k(ay)-\ln^k\left(\frac{a}{y}\right)\right)R(y)dy \end{equation*} in terms of a special function, where $R(y)$ is a general function and $k$ and $a$ are arbitrary complex numbers. These evaluations can be expressed in terms of famous mathematical constants such as the
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