Generalized Nonpolynomial Spline Method by Fractional Order

In this paper, consisted in finding the nonpolynomial spline function and generalized it by fractional order. Other propose of this function was interpolating spline fractional derivatives, with their effective applications to numerically solving fractional boundary value problems. We also discussed the rate of convergence of the method with fractional order. The error bounds and convergence of our difference schemes for nonpolynomial spline with fractional order are theoretically established, this is done by computer program with the aid of the Maptlab 13 for all the above prescribed methods, and the numerical results for boundary value problems are also presented.