Abstract:
In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann-Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS).