A new approach for solving one-dimensional fractional boundary value problems via Haar wavelet collocation method

Abstract

In this paper, we propose the numerical method for positive solutions to the m-point boundary value problems of fractional differential equations with p-Laplacian operator and prove the convergence for our scheme. The operational matrix of fractional integration, based on the accurate calculation of fractional integrals of Haar wavelet functions, is combined with the collocation method and the fixed point iterative method to introduce the function approximation and obtain the approximate solution to the given problem. Also, we present some numerical examples to illustrate our main results.