Generalized fractional operator with applications in mathematical physics

Muhammad Samraiz, Ahsan Mehmood, Sajid Iqbal, Saima Naheed, Gauhar Rahman and Yu-Ming Chu

Chaos, Solitons & Fractals, 2022, vol. 165, issue P2

Abstract: In this paper, we establish a generalize weighted fractional derivative operator involving Mittag-Leffler function in its kernel. This new operator generalizes some well known operators like the Prabhakar fractional derivative. Some significant characteristics of the newly established operator are studied. The weighted fractional derivative and inverse integral of extended hypergeometric function are evaluated. The weighted Laplace transform of fractional derivative operator is obtained. The relationship between weighted and classical Laplace is proved by presenting some examples. The solution of the fractional kinetic differintegral equation is expressed as a series involving the Mittag-Leffler function. The growth model with graphical representation is provided as applications in engineering.

Keywords: Mittag–Leffler; Laplace transform; Modified (k,s)-fractional derivative; Weighted fractional derivative; Fractional kinetic differintegral equation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010098

DOI: 10.1016/j.chaos.2022.112830

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