The main motivation of this study is to extend the use of the operational matrices approach to
solve fractional-order two-point boundary value problems (TPBVPs), a method often …

This paper addresses a new spectral collocation method for solving nonlinear fractional
quadratic integral equations. The main idea of this method is to construct the approximate …

In the present study, a collocation approach based on variouspolynomial basis functions for
solving the nonlinear Riccati differentialequation of fractional-order is presented. Indeed, to …

Volterra integral equation of the second kind with weakly singular kernel usually exhibits
singular behavior at the origin, which deteriorates the accuracy of standard numerical …

This article presents the Chelyshkov wavelet-based numerical technique (CWBNT) for the
solution of the system of non-linear differential equations arising in the study of Darcy …

Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are
employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value …

The main purpose of this paper is to introduce a new formulation of the Tau-collocation
method for solving a class of nonlinear weakly singular delay Volterra integro-differential …

Fractional relaxation-oscillation equation (FROE) has proved to provide more accurate
interpretation of describing materials with viscoelastic properties. However, the current …

in this work, we present an advanced interpolation method via the Vandermonde matrix for
solving weakly singular Volterra integral equations of the second kind. The optimal rules for …

A numerical approach to approximate the nonlinear Burgers' equation solution is presented
in this article. By temporally discretizing the problem using the Crank-Nicolson scheme, we …