An accurate method for solving a singular second-order fractional Emden-Fowler problem

Abstract

In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem. The construction of the reproducing kernel based on orthonormal shifted Legendre polynomials is presented. The validity of the RKHSM is ascertained by presenting several examples. We prove the existence of solution of the singular second-order fractional Emden-Fowler problem. The convergence of the approximate solution using the proposed method is investigated. The uniform convergence of the approximate solution to the exact solution is presented. Error estimation to the proposed method is proven. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems.