Abstract Dengue fever is a common disease which can cause shock, internal bleeding, and death in patients if a second infection is involved. In this paper, a multi-serotype dengue model with nonlinear incidence rate is formulated to study the transmission of two dengue serotypes. The dynamical behaviors of the proposed model depend on the threshold value \(R_{{0}}^{{n}}\) known as the reproductive

Abstract The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black–Scholes equation for a European put option. The Liouville–Caputo derivative was used to improve the ordinary Black–Scholes equation. The analytic solution is a powerful tool for describing the behavior of the option price in the European style

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article by different authors [2] that was simultaneously under consideration at a different journal. The article also shows evidence of authorship manipulation and peer review manipulation. In addition, the identity of the third author could not be verified: the University of Mosul has confirmed that Ahmed

Abstract A synthetic drug transmission model with psychological addicts and time delay is proposed in this paper. By analyzing the corresponding characteristic equation and choosing the time delay as the bifurcation parameter, a set of sufficient criteria guaranteeing local stability of the synthetic drug addiction equilibrium and the appearance of a Hopf bifurcation of the model is established. Further

Abstract In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical

Abstract New nonlinear integral inequalities (NII) are presented in this paper. Based on mathematical analysis technique, several estimation results are obtained, which not only complement the aforementioned results, but also generalize the inequalities to the more general nonlinearities. As an application, they can be employed to estimate the bound on the solutions of power integro-differential equations

Abstract In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold

Abstract Using some fixed point theorems for contractive mappings, including α-γ-Geraghty type contraction, α-type F-contraction, and some other contractions in \(\mathcal{F}\)-metric space, this research intends to investigate the existence of solutions for some Atangana–Baleanu fractional differential equations in the Caputo sense.

Abstract This research work is related to studying a class of special type delay implicit fractional order differential equations under anti-periodic boundary conditions. With the help of classical fixed point theory due to Schauder and Banach, we derive some results about the existence of at least one solution. Further, we also study some results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam

Abstract A simple scheme is proposed for computing \(N \times N\) spectral differentiation matrices of fractional order α for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence relation and is numerically stable. The matrices are then applied to numerically differentiate.

Abstract In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (İşcan in Hacet. J. Math. Stat. 43(6):935–942, 2014 and İşcan and Wu in Appl. Math. Comput. 238:237–244, 2014). We also discuss some special cases for our main results and obtain

Abstract In this paper, we introduce the concept of square-mean piecewise almost automorphic function. By using the theory of semigroups of operators and the contraction mapping principle, the existence of square-mean piecewise almost automorphic mild solutions for linear and nonlinear impulsive stochastic evolution equations is investigated. In addition, the exponential stability of square-mean piecewise

Abstract The aim of present paper is to obtain Shannon type inequalities using the extended version of Jensen’s inequality in time scales settings. The concept of differential entropy of a continuous random variable on time scales is introduced, and its bounds for some particular distributions are also estimated.

Abstract In this work, we develop a high-order composite time discretization scheme based on classical collocation and integral deferred correction methods in a backward semi-Lagrangian framework (BSL) to simulate nonlinear advection–diffusion–dispersion problems. The third-order backward differentiation formula and fourth-order finite difference schemes are used in temporal and spatial discretizations

Abstract The aim of this study is to establish the solution of the time-space fractional Schrödinger equation subject to initial and boundary conditions which has many applications in science such as nonlinear optics, plasma physics, super conductivity, based on the residual power series method (RPSM). We first apply suitable transformations to make the order of one of the fractional derivatives integer

Abstract We consider the generalized KdV–Burgers \(\operatorname{KdVB}(p,m,q)\) equation. We have designed exact and consistent nonstandard finite difference schemes (NSFD) for the numerical solution of the \(\operatorname{KdVB}(2,1,2)\) equation. In particular, we have proposed three explicit and three fully implicit exact finite difference schemes. The proposed NSFD scheme is linearly implicit. The

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article by different authors that was simultaneously under consideration with another journal [2]. In addition, the identity of the corresponding author could not be verified: Universidad Austral confirmed that Tanriver Ülker was never affiliated to this institution. The authors have not responded to any

Abstract In this paper, the parameter identification of gene regulatory network with time-varying delay is studied. Firstly, we introduce the differential equation model of gene regulatory network with unknown parameters and time delay. Secondly, for the unknown parameters in the time-varying model, a corresponding system with adaptive parameters and adaptive controller is introduced, and the parameter

Abstract A coupled Chen–Lee–Liu (CLL) system is proposed and its linear Lax pair is given. Many kinds of nonlocal-derivative NLS (DNLS) equations arise from the group symmetry reductions of the coupled CLL system. \(\hat{P}\hat{T}\hat{C}\)-symmetry invariant one-soliton solution and periodic two-soliton solution of a two-place DNLS (TDNLS) system are obtained. A group symmetry invariant two-soliton

Abstract In this paper, we deal with the inverse problem of identifying the unknown source of time-fractional diffusion equation on a columnar symmetric domain. This problem is ill-posed. Firstly, we establish the conditional stability for this inverse problem. Then the regularization solution is obtained by using the Tikhonov regularization method and the error estimates are derived under the a priori

Abstract This article is devoted to the study of the attractivity of solutions to a class of stochastic evolution equations involving Hilfer fractional derivative. By employing the semigroup theory, fractional calculus and the fixed point technique, we establish new alternative criteria to ensure the existence of globally attractive solutions for the Cauchy problem when the associated semigroup is

Abstract In this paper, we propose a single species logistic model with feedback control and additive Allee effect in the growth of species. The basic aim of the paper is to discuss how the additive Allee effect and feedback control influence the above model’s dynamical behaviors. Firstly, the existence and stability of equilibria are discussed under three different cases, i.e., weak Allee effect,

Abstract In this paper, we introduce the generalized k-fractional integral in terms of a new parameter \(k>0\), present some new important inequalities of Pólya–Szegö and Čebyšev types by use of the generalized k-fractional integral. Our consequences with this new integral operator have the abilities to implement the evaluation of many mathematical problems related to real world applications.

Abstract Stochastic differential models provide an additional degree of realism compared to their corresponding deterministic counterparts because of the randomness and stochasticity of real life. In this work, we study the dynamics of a stochastic delay differential model for prey–predator system with hunting cooperation in predators. Existence and uniqueness of global positive solution and stochastically

Abstract In our article, a nonlinear density-dependent mortality Nicholson’s blowflies system with patch structure has been investigated, in which the delays are time-varying and multiple pairs. Based upon the fluctuation lemma and differential inequality techniques, some sufficient conditions are found to ensure the global asymptotic stability of the addressed model. Moreover, a numerical example

Abstract This paper explores a class of unbounded distributed delayed inertial neural networks. By introducing some new differential inequality analysis and abandoning the traditional order reduction technique, some new assertions are derived to verify the global exponential stability of the addressed networks, which improve and generalize some recently published articles. Finally, two cases of numerical

Abstract In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial condition. We acquire some conditions for existence, uniqueness, Ulam–Hyers, and Ulam–Hyers–Rassias stability. Modified Gronwall’s inequality is presented

Abstract In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter–Saxton equation, a time fractional nonlinear diffusion equation, a time fractional

Abstract A finite-time adaptive neural network position tracking control method is considered for the fractional-order chaotic permanent magnet synchronous motor (PMSM) via command filtered backstepping in this paper. Firstly, a neural network with a fractional-order parametric update law is utilized to cope with the nonlinear and unknown functions. Then the command filtered technique is introduced

Abstract In this paper, we analytically and numerically study the dynamics of a stochastic toxin-producing phytoplankton–fish system with harvesting. Mathematically, we give the existence and stability of the positive equilibrium in the deterministic system (i.e., the system without environmental noise fluctuations). In the case of the stochastic system (i.e., the system with environmental noise fluctuations)

Abstract The Zhang neural network (ZNN) has become a benchmark solver for various time-varying problems solving. In this paper, leveraging a novel design formula, a noise-tolerant continuous-time ZNN (NTCTZNN) model is deliberately developed and analyzed for a time-varying Lyapunov equation, which inherits the exponential convergence rate of the classical CTZNN in a noiseless environment. Theoretical

Abstract In this paper, we extend formal and analytic normal forms from autonomous difference systems to non-autonomous ones based on the uniform dichotomy spectrum of their linear part.

Abstract In this paper, we study the local and global existence, and uniqueness of mild solution to initial value problems for fractional semilinear evolution equations with compact and noncompact semigroup in Banach spaces. In particular, we derive the form of fundamental solution in terms of semigroup induced by resolvent and ψ-function from Caputo fractional derivatives. These results generalize

Abstract In this paper, based on the model of Zhao, Qin, and Chen [Adv. Differ. Equ. 2018:172, 2018], we propose a new model of the May cooperative system with strong and weak cooperative partners. The model overcomes the drawback of the corresponding model of Zhao, Qin, and Chen. By using the differential inequality theory, a set of sufficient conditions that ensure the permanence of the system are

Abstract In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients. In more detail, we introduce degenerate generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involve powers of λ-binomial coefficients and λ-falling sequence, and can be represented

Abstract This paper is devoted to studying the growth of entire or meromorphic solutions to two systems of q-difference differential equations. The estimates on the growth order of meromorphic solutions are obtained, which are extensions of previous results due to Xu et al . Examples are given to illustrate the existence of solutions of such systems.

This paper concerns the problem of enhanced results on robust finite time passivity for uncertain discrete time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, reciprocally convex combination method, and linear matrix inequality technique, we derive several sufficient conditions for varying the passivity of discrete

This paper is concerned with the existence of entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text]. With the aid of the comparison theorem and the sup-sub solutions method, we construct some entire solutions that behave as two opposite traveling front solutions with critical

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens type.

We establish analogues of the mean value theorem and Taylor's theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying

In this article, we deduce a uniqueness result of entire functions that share a small entire function with their two difference operators, generalizing some previous theorems of (Farissi et al. in Complex Anal. Oper. Theory 10:1317-1327, 2015, Theorem 1.1) and (Chen and Li in Adv. Differ. Equ. 2014:311, 2014, Theorem 1.1) by omitting the assumption that the shared small entire function is periodic

In this paper, the fuzzy [Formula: see text] output-feedback control problem is investigated for a class of discrete-time T-S fuzzy systems with channel fadings, sector nonlinearities, randomly occurring interval delays (ROIDs) and randomly occurring nonlinearities (RONs). A series of variables of the randomly occurring phenomena obeying the Bernoulli distribution is used to govern ROIDs and RONs.

The present paper deals with the problem of an ecoepidemiological model with linear mass-action functional response perturbed by white noise. The essential mathematical features are analyzed with the help of the stochastic stability, its long time behavior around the equilibrium of deterministic ecoepidemiological model, and the stochastic asymptotic stability by Lyapunov analysis methods. Numerical

In this article, for delayed Nicholson's blowflies equation, we propose a hybrid control nonstandard finite-difference (NSFD) scheme in which state feedback and parameter perturbation are used to control the Neimark-Sacker bifurcation. Firstly, the local stability of the positive equilibria for hybrid control delay differential equation is discussed according to Hopf bifurcation theory. Then, for any