Legendre Collocation Method for the Nonlinear Space–Time Fractional Partial Differential Equations

Abstract

In this study, nonlinear space–time fractional partial differential equations with variable coefficients are considered. The fractional derivatives are described in the conformable sense and Caputo sense. The numerical approach is based on the shifted Legendre polynomials and the finite difference method. Several illustrative examples are given to observe the validity, effectiveness and accuracy of the present numerical method.