Application of Green's function and Sinc approximation in the numerical solution of the fractional differential equations

The primary purpose of this paper is the construction of the Green's function and Sinc approximation for a class of Caputo fractional boundary value problems (CFBVPs). By using the inverse derivative of the fractional order, we can derive the equivalent fractional order Volterra integral equations from CFBVPs, which is considered Green's function. It is approximated by the Sinc-Collocation method. A convergence analysis of the presented method is given. Our approach is applied to five examples.  We derive that our approach converges to the exact solution rapidly with the order of exponential accuracy.

Keywords:

Volterra integral equations , Sinc-collocation method , Green's function , fractional boundary value problems , fractional integrals