A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach (Fractional Calculus and Applied Analysis, ...

This paper investigates the solution to one-dimensional fractional differential equations with two types of derivative operators orders in range (1,2). Two linearized schemes numerical method are constructed. The considered FDEs equivalently transformed by Riemann–Liouville integral into their integro-partial problems reduce requirement for smoothness time. analysis stability and convergence is...

A relatively new and efficient approach based on a iterative method the Aboodh transform called is proposed to solve space-time fractional differential equations, order considered in Caputo sense. This combination of gives solution series form with easily computable components. The nonlinear term handled by method, affirm simplicity performance five examples were considered, plots presented sho...

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for th...

‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given an...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...