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 …

In the current study, a novel and effective method for solving the nonlinear fractional mixed
partial integro-differential equation (NfrPIo-DE) based on a continuous kernel is presented …

In this article, two numerical techniques, namely, the homotopy perturbation and the matrix
approach methods have been proposed and implemented to obtain an approximate solution …

By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine
the existence of solutions for fractional integral equations, which include as special cases of …

This article solves the nonlinear fractional integral equation (NFrIE) using the Genocchi
polynomial method (GPM). We have provided proof to demonstrate the existence of a …

Two numerical methods based on Laguerre and Touchard polynomials are described in this
paper to solve both the fractional integral equations of the first kind and the second kind …

We extend the virtual element method to the two-dimensional time-fractional parabolic PDE,
characterized by a fractional derivative of order α∈(0, 1) in time. To illustrate the working of …

We introduce a numerical method for approximating the solutions of φ− fractional differential
equations. The method employs a generalization of the Lagrange polynomial to …

In this article, two numerical methods based on Touchard and Laguerre polynomials were
presented to solve Abel integral (AI) equations. Touchard and Laguerre matrices were …

A novel iterative numerical method is constructed for solving second kind Volterra fractional
integral equations. The method uses at each iterative step a Bernstein spline interpolation …