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In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global posit...
Anti-viral therapy is comparatively very effective for patients who get affected by the hepatitis B virus. It is of prime importance to understand the different relations among the viruses, immune responses an...
In this paper, we investigate a 3-D diffusion equation within the scope of the local fractional derivative. For this model, we establish local fractional vector operators and a local fractional Laplace operato...
The stochastic resonance (SR) of a second-order harmonic oscillator subject to mass fluctuation and periodic modulated noise in viscous media is studied. The mass fluctuation noise is modeled as dichotomous no...
In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fra...
In this paper, we study the numerical methods for solving the time-fractional Schrödinger equation (TFSE) with Caputo or Riemann–Liouville fractional derivative. The numerical schemes are implemented by using ...
In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As a...
We consider distributed-order partial differential equations with time fractional derivative proposed by Caputo and Fabrizio in a one-dimensional space. Two finite difference schemes are established via Grünwa...
This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs)...
The key objective of this paper is to study and discuss the application of fractional calculus on an arbitrary-order inventory control problem. Using the concepts of fractional calculus followed by fractional ...
In this paper, we establish new oscillation criteria for nonlinear second order difference equations with mixed neutral terms. The key idea of our approach is to compare with first order equations whose oscill...
To improve the computing efficiency, a fourth-order difference scheme is proposed and a fast algorithm is designed to simulate the nonlinear fractional Schrödinger (FNLS) equation oriented from the fractional ...
In this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are descr...
The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivativ...
In this paper, we investigate the fractional Schödinger equation involving a critical growth. By using the principle of concentration compactness and the variational method, we obtain some new existence result...
The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error prin...
In this paper, the sine-Gordon expansion method is used to obtain analytical solutions of the conformable space-time generalized reaction Duffing model and conformable space-time Eckhaus equation with the aid ...
In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary v...
The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this p...
In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of ph...
The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with im...
In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, di...
The fractional sub-diffusion equation, which is obtained by replacing the time derivative in ordinary diffusion by a fractional derivative of order ϑ with
...
In recent years, many research works have been focusing on the propagation dynamics of infectious diseases in complex networks, and some interesting results have been obtained. The main purpose of this paper i...
The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo–Fabrizio fractional operator for the inclus...
This paper outlines further properties concerning the fractional derivative of the Riemann ζ function. The functional equation, computed by the introduction of the Grünwald–Letnikov fractional derivative, is rewr...
In this paper, an optimal control for a novel fractional West Nile virus model with time delay is presented. The proposed model is governed by a system of fractional delay differential equations, where the fra...
In this manuscript, we talk over the existence of solutions of a class of hybrid Caputo–Hadamard fractional differential inclusions with Dirichlet boundary conditions. Our results are based on the Arzelá–Ascol...
One of the interesting fractional integro-differential equations is the three step crisis equation which has been reviewed recently. In this paper, we investigate the existence of solutions for a three step cr...
In this paper, we compare solutions of q-order fractional differential equations of Caputo type for q near 1 with solutions of the corresponding 1-order ordinary differential equations. By establishing the explic...
In this paper, we establish some Lyapunov-type inequalities for a class of linear and nonlinear fractional q-difference boundary value problems under Cauchy boundary conditions. As applications, we use the inequa...
In this article, we study a coupled system of singular fractional difference equations with fractional sum boundary conditions. A sufficient condition of the existence of positive solutions is established by e...
In this paper, we present a semi-analytic method called the local fractional homotopy analysis method (LFHAM) for solving differential equations involving local fractional derivatives based on the local fracti...
A new approximate technique is introduced to find a solution of FVFIDE with mixed boundary conditions. This paper started from the meaning of Caputo fractional differential operator. The fractional derivatives...
This paper studied the existence and uniqueness of the solution of the fractional logistic differential equation using Hadamard derivative and integral. Previous work has shown that there is not an exact solut...
This paper introduces the solution of differential algebraic equations using two hybrid classes and their twin one-leg with improved stability properties. Physical systems of interest in control theory are som...
In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to o...
A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS metho...
New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to ...
It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically pr...
This paper focuses on the Caputo fractional differential system involving coupled integral boundary conditions and parameters. Using the properties of the Green function, the Leray–Schauder’s alternative and t...
The primary motivation of this paper is to extend the application of the reproducing-kernel method (RKM) and the residual power series method (RPSM) to conduct a numerical investigation for a class of boundary...
In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operato...
In this paper, a new generalized exponential rational function method is employed to extract new solitary wave solutions for the Zakharov–Kuznetsov equation (ZKE). The ZKE exhibits the behavior of weakly nonli...