Article ID: MTJPAM-D-23-00033

Title: A general family of hybrid-type fractional-order kinetic equations involving the Liouville-Caputo fractional derivative


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00033; Volume 6 / Issue 3 / Year 2024, Pages 48-61

Document Type: Research Paper

Author(s): ‪Hari Mohan Srivastava a, b, c, d, e, f

aDepartment of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

bDepartment of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China

cCenter for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

dDepartment of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan, Republic of China

eDepartment of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan

fSection of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy

Received: 17 October 2023, Accepted: 17 October 2023, Published: 28 October 2023

Corresponding Author: ‪Hari Mohan Srivastava (Email address: harimsri@math.uvic.ca)

Full Text: PDF

Abstract

This article is motivated essentially by the fact that, in the current literature, many different kinds of operators of fractional calculus (that is, fractional-order integrals and fractional-order derivatives) have been and continue to be successfully applied in the modeling and analysis of a considerably large number of applied scientific and real-world problems in the mathematical, physical, biological, engineering and statistical sciences, and indeed in other scientific disciplines as well. We aim here at investigating a general family of hybrid-type fractional-order kinetic equations, which is associated with the Liouville-Caputo (LC) fractional derivative. Our main results are sufficiently general in character and are capable of furnishing solutions of a remarkably large number of simpler fractional-order kinetic equations.

Keywords: Riemann-Liouville and related fractional integral and fractional derivative operators, Liouville-Caputo fractional derivative operator, Hypergeometric functions, special (or higher transcendental) functions, Fox-Wright hypergeometric function, Mittag-Leffler type functions, general Fox-Wright function, Zeta and related functions, Lerch transcendent (or Hurwitz-Lerch zeta function)

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