B-spline operational matrix of fractional integration

In this paper, we use the second and third order spline functions to derive the operational matrix of fractional integration, which we then apply to solve fractional integro-differential equations, Abel equations and partial fractional differential equations. We also present a method based on the dual functions of B-spline functions to solve fractional equations. This method results in an algebraic system that we can solve easily. Finally, we present illustrative examples to demonstrate the applicability of our method and compare it with other known ones.