Sinc-Galerkin method for solving higher order fractional boundary value problems

In this work we use the sinc-Galerkin method to solve higher order fractional boundary value problems. We estimate the second order fractional derivative in the Caputo sense. More precisely, we find a numerical solution for g1(t)D^αu(t) + g2(t)D^βu(t) + p(t)u⁽⁴⁾(t) + q(t)u(t) = f(t), 0 < t < 1, 0 < β < 1, 1 < α < 2, subject to the boundary conditions u(0) = 0, u⁰(0) = 0, u(1) = 0, u⁰(1) = 0. Our contribution appears in the estimate of D^αu for higher order α. Numerical examples are described to show the accuracy of this attempt where we applied the sinc-Galerkin method for fractional order differential equations with singularities.