‎This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by u...

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative...

A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method VIM nor polynomials like Adomian’s decomposition method ADM so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the li...

In this paper, Sumudu decomposition method is developed to solve general form of fractional partial differential equation. The proposed method is based on the application of Sumudu transform to nonlinear fractional partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivatives are described in the Caputo sense. The Sumud...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

In this work, we obtain a Lyapunov-type inequality for a\ fractional differential equation involving Caputo derivatives of higher order and subject to nonlocal boundary conditions. An application eigenvalue problems is also given.

The fractional calculus is one of the active research fields in mathematical analysis, primarily from its importance in modeling of various problems in engineering, physics, chemistry and other sciences. Presumably the first systematic exposition on abstract time-fractional equations with Caputo fractional derivatives is that of Bazhlekova [2]. In this fundamental work, the abstract time-fracti...

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

A numerical framework based on fuzzy finite difference is presented for approximating triangular solutions of partial differential equations by considering the type $$[gH-p]-$$ differentiability. The triangle functions are expanded using full Taylor expansion to develop a new method. By gH-differentiability, we approximate derivatives with difference. In particular, propose this method solve no...