Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative

Abstract

In this paper, it is presented that an approximate solution of a class of non-linear differential equations with conformable derivative under boundary conditions by using sinc-Galerkin method that is not used to approximately solve the class of the considered equation in the literature. In the method, the solution function is expressed as a finite series in terms of composite translated sinc functions and the unknown coefficients. The problem is reduced into a non-linear matrix-vector system via sinc grid points, and when this system is solved by using Newton's method, the unknown coefficients of the solution function are easily obtained. Also, error analysis and some test problems are presented to illustrate the applicability and accuracy of the proposed method.