Abbas Saadatmandi

TL;DR: The main aim is to generalize the Legendre operational matrix to the fractional calculus and reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem.

TL;DR: In this paper, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations (FPDE) with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives, and the results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

TL;DR: In this paper, an approximation technique based on the shifted Legendre-tau idea is presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain.

TL;DR: In this article, the numerical solution of classes of fractional convection-diffusion equations with variable coefficients is solved by reducing the problem to the solution of linear algebraic equations by expanding the required approximate solution as the elements of shifted Legendre polynomials in time and the Sinc functions in space with unknown coefficients.

TL;DR: A numerical scheme to solve the one‐dimensional hyperbolic telegraph equation by expanding the required approximate solution as the elements of shifted Chebyshev polynomials using the operational matrices of integral and derivative.