Cubic B-Spline Finite Element Method for Fractional Ordinary Differential Equations

The paper offers a numerical approximation for fractional ordinary differential equations in which the first and second-order are replaced by a fractional derivative. We have employed the cubic B-spline approach coupled with the finite element approach to sort out such problems. Also discussed exploring fractional differential equations by proving the existence and uniqueness of their solutions, along with the correctness of their error estimations. The error estimation is derived by the Aubin–Nitsche duality argument. The efficiency of all the proposed approaches is compared in several numerical examples in order to verify, demonstrate and display the applicability of the approach, as well as to compare the estimated outcomes with analytical result.