The time-fractional diffusion equation is applied to a wide range of practical applications. We
suggest using a potent spectral approach to solve this equation. These techniques' main …

This research work is dedicated to an investigation of the existence and uniqueness of a
class of nonlinear ψ-Caputo fractional differential equation on a finite interval [0, T] …

An efficient technique, called pseudo-Galerkin, is performed to approximate some types of
linear/nonlinear BVPs. The core of the performance process is the two well-known weighted …

This article aims to present a new approach based on the operational matrix method for
solving integro-differential equations using numerical techniques. In this method, we employ …

New modified shifted Chebyshev polynomials (MSCPs) have been constructed over the
interval [α, β]. These polynomials are utilized as basis functions with the application of the …

This paper is primarily concern with the formulation and analysis of a reliable numerical
method based on the novel alternating direction implicit finite difference scheme for the …

An investigation of two nonlinear mixed Volterra–Fredholm integral equations of the second
kind is undertaken. The equations are constructed as fixed-point problems, under the …

An efficient numerical algorithm is developed for solving nonlinear functional Volterra
integral equations. The core idea is to define an appropriate operator, then combine the …

An algorithm based on a class of the Chebyshev polynomials family called the fifth-kind
Chebyshev polynomials (FCPs) is introduced to solve the multi-term variable-order time …

A high accurate spectral algorithm for two-dimensional nonlinear reaction-diffusion equation
with Riesz space-fractional (RF-TNRDEs) is consider. We propose a shifted Legendre …