Approximate solution of nonlinear quadratic integral equations of fractional order via piecewise linear functions

Abstract

In this paper, the main objective is to describe an approximate scheme for solving nonlinear quadratic integral equations (NQIEs) of fractional order. The method is based on piecewise linear functions that are called hat functions (HFs). By applying the HFs approximation, their properties and operational matrices, nonlinear equation becomes to a nonlinear system of equations which can be solved by using simple arithmetic methods. Also, the error analysis of HFs method and convergence analysis of proposed model are given. At the end, two nonlinear examples are presented to illustrate the validity and applicability of the explained approach.