On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function

Muhammad Samraiz, Ahsan Mehmood, Saima Naheed, Gauhar Rahman, Artion Kashuri and Kamsing Nonlaopon ()
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Muhammad Samraiz: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Ahsan Mehmood: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Saima Naheed: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Gauhar Rahman: Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan
Artion Kashuri: Department of Mathematics, Faculty of Technical and Natural Sciences, University Ismail Qemali, 9400 Vlora, Albania
Kamsing Nonlaopon: Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2022, vol. 10, issue 21, 1-19

Abstract: The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional operators, such as the semi-group and inverse characteristics, are studied. As special cases of these novel fractional operators, several fractional operators that are already well known in the literature are acquired. The generalized Laplace transform of these operators is evaluated. By involving the explored fractional operators, a kinetic differintegral equation is introduced, and its solution is obtained by using the Laplace transform. As a real-life problem, a growth model is developed and its graph is sketched.

Keywords: multivariate Mittag–Leffler; fractional integral; fractional derivative; generalized Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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