A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems

Abstract

In this article, a new reproducing kernel approach is developed for obtaining a numerical solution of multi-order fractional nonlinear three-point boundary value problems. This approach is based on a reproducing kernel, which is constructed by shifted Legendre polynomials (L-RKM). In the considered problem, fractional derivatives with respect to α and β are defined in the Caputo sense. This method has been applied to some examples that have exact solutions. In order to show the robustness of the proposed method, some examples are solved and numerical results are given in tabulated forms.

An effective approach for numerical solution of linear and nonlinear singular boundary value problems

“…4 Rashidinia et al 5 developed the Sinc-Galerkin method for the numerical solution of SBVP. There are different researches such as other studies 6,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] in the literature for the numerical solutions of differential equations.…”

New Challenges Arising in Engineering Problems with Fractional and Integer Order

“…In [10], a new reproducing kernel approach was developed to obtain a numerical solution for multi-order fractional nonlinear three-point boundary value problems. This approach was based on a reproducing kernel, which was constructed by shifted Legendre polynomials (L-RKM).…”