A scalar nonlinear impulsive differential equation with a delay and generalized proportional Caputo fractional derivatives (IDGFDE) is investigated. The linear boundary value problem (BVP) for the given set up. explicit form of unique solution BVP in special case obtained. This formula generalization without any as well derivatives. Furthermore, this integral used to define operator applied det...

This work is devoted to prove the existence and uniqueness of solution BVP with non-local assumptions on boundary integral gluing conditions for parabolic-hyperbolic type equation involving Caputo derivatives. Using method energy, have been proved. Existence was proved by equations

In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find solution nonlinear fractional Gardner and Cahn–Hilliard equations arising in fluid flow. The derivative is considered an Atangana–Baleanu Caputo manner (ABC) Caputo–Fabrizio (CF) throughout paper. We implement transform aid of suggested obtain followed by inverse transform. To show accuracy va...

In the Present manuscript we have investigate the Adaptive projective synchronization between different fractional order chaotic systemsusing modified adaptive control method with unknown parameters. The modified adaptive control method is very affective and more convenient in compression to the existing method for the synchronization of the fractional order chaotic systems. The chaotic attract...

In this paper, we consider a fractional model of telegraph equation in terms of voltage and current. The fractional derivatives are taken in the Caputo sense. The numerical algorithm based on the homotopy perturbation transform method (HPTM) is applied to obtain analytic and approximate solutions of the space-time fractional telegraph equations. The HPTM is combined in the form of Laplace trans...

Abstract: In this paper, we study the approximation of analytical solution for Fractional Reaction Diffusion model which describes the evaluation of bacterium Bacillus, which grows on the surface of thin agar plates, by using homotopy analysis transform method. The fractional derivatives are described by caputo sense. A comparative study between the homotopy analysis transform method and the cl...

In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results r...

*Correspondence: [email protected]; [email protected]; [email protected] 1Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China 2School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland Abstract In this paper, we investigate the existence of local center stable manifolds of Langevin differential equations wi...

We investigate a new class of boundary value problems nonlinear coupled system sequential fractional differential equations and inclusions involving Caputo derivatives conditions. use standard fixed-point theory tools to deduce sufficient criteria for the existence uniqueness solutions at hand. Examples are discussed illustrate validity proposed results.

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...