For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …

Recently there has been a growing interest in designing efficient numerical methods for the
solution of fractional differential equations. The solutions of such equations in general …

This paper develops and analyses a finite difference/spectral-Galerkin scheme for the
nonlinear fractional Schrödinger equations with Riesz space-and Caputo time-fractional …

Due to the lack of a discrete fractional Grönwall-type inequality, the techniques of analyzing
the L 2− 1 σ difference schemes would not be correct to apply directly to the nonlinear multi …

This paper is devoted to introducing a novel methodology to prove the convergence and
stability of a Crank–Nicolson difference approximation for a class of multi-term time …

In this study, an efficient semi-discrete method based on the two-dimensional Legendre
wavelets (2D LWs) is developed to provide approximate solutions of nonlinear variable …

The theoretical analysis (convergence and stability) of an L 2− 1 σ difference method is
presented for nonlinear time-fractional diffusion equations with multiple delays. In this …

In this paper, compact finite difference schemes with (3-α)-th order accuracy in time and
fourth order accuracy in space based on the L 1 method are constructed for time-fractional …

This paper investigates a nonlinear time-fractional mixed sub-diffusion and diffusion-wave
equation with delay. The problem is particularly challenging due to its nonlinear nature, the …

In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre
spectral scheme for the nonlinear multiterm Caputo time fractional‐order reaction‐diffusion …