A study of the right local general truncated $M$-fractional derivative
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 503-520
https://doi.org/10.4134/CKMS.c210098
Published online March 29, 2022
Printed April 30, 2022
Rajendrakumar B. Chauhan, Meera H. Chudasama
Charotar University of Science and Technology; Charotar University of Science and 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 viz. 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 a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.
Keywords : Generalized derivatives, mean value theorems, truncated Mittag-Leffler function, conformable fractional derivative, alternative fractional derivative, truncated $M$-fractional derivative, right local general $M$-fractional derivative
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