Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2021.03.19
  • Accepted : 2021.05.17
  • Published : 2022.04.30
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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.

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Acknowledgement

Authors sincerely thank the referees for going through the manuscript critically and giving the valuable comments for the improvement of the manuscript.

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