Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2022; 37(2): 503-520

Online first article March 29, 2022      Printed April 30, 2022

https://doi.org/10.4134/CKMS.c210098

Copyright © The Korean Mathematical Society.

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

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

MSC numbers: 26A06, 26A24, 26A33, 26A42, 33E12

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