Spline solutions of linear fractional bvps with two caputos approaches

Abstract

In this paper, an efficient numerical methods based on cubic polynomial spline functions are proposed for the linear fractional boundary value problems (FBVPs) with Caputos left and right fractional operator. In computing the approximation to the solutions of FBVPs, consistency relations have been derived with the help of spline functions. For convergence analysis of this method, it is assumed that the exact solu- tion of FBVP belongs to a class of C⁶ -functions. Numerical examples are considered to illustrate the accuracy and efficiency of this method and compare the results with other methods developed by Akram and Tariq in [18] and Zahra and Elkholy in [28-30].