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