Numerical solution of fractional Bratu type equations with Legendre reproducing kernel method

TL;DR

This paper introduces a novel numerical method combining reproducing kernel Hilbert space theory and Legendre polynomials to efficiently solve fractional Bratu boundary value problems with Caputo derivatives.

Contribution

The paper presents a new iterative reproducing kernel method using shifted Legendre polynomials for fractional Bratu equations, including proof of convergence.

Findings

Method is effective for fractional Bratu problems.

Numerical results demonstrate accuracy and convenience.

Convergence of the iterative process is established.

Abstract

In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert space theory with shifted Legendre polynomials. Construction and convergence of iterative process are shown by orthogonal projection operator. Numerical results show that our method is effective and convenient for fractional Bratu type problem.