Fractional-order B-spline functions for solving fractional-order differential equations

In this article, a general formulation for the fractional-order B-spline functions is con- structed to obtain the solution of the fractional-order differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. Our main aim is to generalize the new orthonormal functions based on B-spline functions to the fractional calculus operational matrices is driven. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations.