In this article, we construct an efficient numerical algorithm with the second-order time
accuracy for a two-dimensional nonlinear fourth-order fractional wave equation. We …

In the present work, a high-order numerical scheme is proposed and analyzed to solve the
non-linear time fractional reaction–diffusion equation (RDE) of order α∈(0, 1). The …

In the present study, we introduce a high-order non-polynomial spline method designed for
non-linear time-fractional reaction–diffusion equations with an initial singularity. The method …

Introduction Recently, a new family of fractional derivatives called the piecewise fractional
derivatives has been introduced, arguing that for some problems, each of the classical …

In this paper, we deal with the nonlinear fractional pseudo‐parabolic equations (FPPEs). We
propose an accurate numerical algorithm for solving the aforementioned well‐known …

We construct a compact difference scheme for two-dimensional time-fractional nonlinear
fourth-order diffusion equation with time delay. By choosing the second-order spatial …

In this article, a local meshless technique is applied for numerical simulation of multi-
dimensional Galilei invariant fractional advection–diffusion model on regular and irregular …

In this article, we discuss the fractional temporal-spatial reaction-diffusion model with
Neumann boundary conditions in one-and two-dimensional cases. The problem is solved by …

In this article, we study a class of two-dimensional nonlinear fourth-order partial differential
equation models with the Riemann–Liouville fractional integral term by using a mixed …

In this article, an accurate optimization algorithm based on new polynomials namely
generalized shifted Vieta-Fibonacci polynomials (GSVFPs) is employed to solve the …