This paper is concerned with a numerical procedure for fractional Volterra integro-differential
equations with weakly singular kernels. The fractional derivative is in the Caputo sense. In …

The book presents efficient numerical methods for simulation and analysis of physical
processes exhibiting fractional order (FO) dynamics. The book introduces FO system …

In this paper, we propose the triangular orthogonal functions as a basis functions for solution
of weakly singular Volterra integral equations of the second kind. Powerful properties of …

The reproducing kernel method and Taylor series to determine a solution for nonlinear
Abel's integral equations are combined. In this technique, we first convert it to a nonlinear …

In this paper, single-term Walsh series (STWS) method is applied to obtain the numerical
solutions of Hammerstein systems of nonlinear Volterra integral equations of second kind …

In this paper, a modified Taylor wavelet method (MTWM) is developed for numerical
solutions of various types of Abel's integral equations. This method is based on the modified …

This paper considers the Galerkin spectral method for solving linear second‐kind Volterra
integral equations with weakly singular kernels on large intervals. By using some variable …

The objective of the present article to derive the operational matrices for fractional
integration based on different wavelets. By using this approach, we find the operational …

In this note, we propose a new class of orthogonal polynomials (named Bachok–Hasham
polynomials H 1 nk (x)), which is an extension of the Chebyshev polynomials …

In this paper, we use the concept of homotopy, Laplace transform, and He's polynomials, to
propose the auxiliary Laplace homotopy parameter method (ALHPM). We construct a …