Extended fractional derivative: Some results involving classical properties and applications

Published

20-12-2024

DOI:

https://doi.org/10.58414/SCIENTIFICTEMPER.2024.15.4.09

Keywords:

Caputo fractional derivative, Riemann-Liouville fractional derivative, Extended fractional derivative, Conformable fractional derivative.

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Issue

Section

SECTION B: PHYSICAL SCIENCES, PHARMACY, MATHS AND STATS

Authors

  • Rajratana Maroti Kamble Department of Mathematics, Shri Vitthal Rukmini Arts, Commerce and Science College, Yavatmal, Maharashtra, India.
  • Pramod Ramakant Kulkarni Department of Mathematics, NES Science College, Nanded, Maharashtra, India.

Abstract

In this paper, considering the classical definition of derivative in the limit form, we can define a new fractional derivative called the extended fractional derivative, which depends upon two parameters α and a. For this new fractional derivative, we have proved the properties of classical derivatives such as the product rule, the quotient rule, the chain rule, Rolle’s and Lagrange’s mean value theorems, etc., which are nor satisfied by the existing fractional derivatives defined by Riemann Liouville, Caputo, Grunwald. Moreover, we have defined the extended fractional integral and proved some related results. Solve extended fractional differential equation.

How to Cite

Rajratana Maroti Kamble, & Kulkarni, P. R. (2024). Extended fractional derivative: Some results involving classical properties and applications. The Scientific Temper, 15(04), 3026–3033. https://doi.org/10.58414/SCIENTIFICTEMPER.2024.15.4.09

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