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http://dx.doi.org/10.4134/CKMS.c210098

A STUDY OF THE RIGHT LOCAL GENERAL TRUNCATED M-FRACTIONAL DERIVATIVE  

Chauhan, Rajendrakumar B. (Department of Mathematical Sciences P. D. Patel Institute of Applied Sciences Charotar University of Science and Technology)
Chudasama, Meera H. (Department of Mathematical Sciences P. D. Patel Institute of Applied Sciences Charotar University of Science and Technology)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.2, 2022 , pp. 503-520 More about this Journal
Abstract
We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-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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