A study of the right local general truncated $M$-fractional derivative

Commun. Korean Math. Soc. Published online July 22, 2021

RAJENDRAKUMAR B CHAUHAN and MEERA H CHUDASAMA
P. D. Patel Institute of Applied Sciences, CHAROTAR UNIVERSITY OF SCIENCE & TECHNOLOGY; P. D. Patel Institute of Applied Sciences, CHAROTAR UNIVERSITY OF SCIENCE & TECHNOLOGY

Abstract : We introduce a new type of fractional derivative, which we call as the right local general truncated $M$-fractional derivative for $\alpha$-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus like the Rolle's theorem, the Mean Value Theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative we describe the application containing an analytic solution of the Kirchoff's voltage law with the help of MATLAB software.

Keywords : Truncated Mittag-Leffler function, Conformable Fractional derivative, Alternative Fractional derivative, Truncated $M$-Fractional derivative, Right local general $M$-Fractional derivative