An Efficient Approach for Solving Differential Equations in the Frame of a New Fractional Derivative Operator

Recently, a new fractional derivative operator has been introduced so that it presents the combination of Riemann–Liouville integral and Caputo derivative. This paper aims to enhance reproducing kernel Hilbert space method (RKHSM, for short) solving certain differential equations involving this is first time application RKHSM employed some with operator. We illustrate convergence analysis applicability reliability suggested approaches. The results confirm finds true solution. Additionally, these numerical indicate effectiveness proposed method.