ON WEIGHTED k-FRACTIONAL OPERATORS WITH APPLICATIONS IN MATHEMATICAL PHYSICS

Shanhe Wu (), Muhammad Samraiz (), Zahida Perveen (), Sajid Iqbal () and Azhar Hussain
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Shanhe Wu: Department of Mathematics, Longyan University, Longyan 364012, P. R. China
Muhammad Samraiz: Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Zahida Perveen: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Sajid Iqbal: Department of Mathematics, Riphah International University, Faisalabad Campus, Satyana Road, Faisalabad, Pakistan
Azhar Hussain: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-14

Abstract: The main objective of this paper is to present weighted k-fractional integral and derivative operators of a function with respect to another function and to uncover their properties. In addition to this, we find the weighted Laplace transform of the newly defined operators. As applications of the weighted k-fractional operators in mathematical physics, we study the fractional forms of kinetic differintegral equation and the time-fractional heat equation involving the novel operators and find their solutions using weighted Laplace transform.

Keywords: Weighted k-Prabhakar Fractional Integral Operator; Weighted k-Prabhakar Fractional Derivative; Weighted k-Caputo Fractional Derivative (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500845

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