In this paper, under some conditions in the Banach space C ([0, β], R), we establish the
existence and uniqueness of the solution for the nonlinear integral equations involving the …

This investigation is concerned with the solutions of Volterra integral equations of second
kind that have been determined by employing Optimal Homotopy Asymptotic method …

In this study, an effective numerical approach based on the hybrid of block-pulse and
parabolic functions (PBPFs) is suggested to obtain an approximate solution of a system of …

In this paper, we first preset two-dimensional Bernstein polynomials operational matrix
(2DBPOM) for two-dimensional fractional integral equations (2DFIE). Then, we introduce a …

In this paper, by combined homotopy analysis method and Laplace transform method, we
produce a new powerful method and named homotopy analysis transform method. By using …

This article concerns with a computational scheme to solve two-dimensional stochastic
fractional integral equations (2DSFIEs), numerically. In these equations, the fractional …

The main aim of the present work is to propose a new and simple algorithm for Abel integral
equation, namely homotopy perturbation transform method (HPTM). The homotopy …

A Haar wavelet operational matrix is applied to fractional integration, which has not been
undertaken before. The Haar wavelet approximating method is used to reduce the fractional …

We propose the generalized quadrature methods for numerical solution of singular integral
equation of Abel type. We overcome the singularity using the analytic computation of the …

In this attempt, we introduce a new technique to solve main generalized Abel's integral
equations and generalized weakly singular Volterra integral equations analytically. This …