Distributional Representation of a Special Fox–Wright Function with an Application

Asifa Tassaddiq, Rekha Srivastava (), Ruhaila Md Kasmani and Dalal Khalid Almutairi
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Asifa Tassaddiq: Department of Basic Sciences and Humanities, College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia
Rekha Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Ruhaila Md Kasmani: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Dalal Khalid Almutairi: Department of Mathematics, College of Education, Majmaah University, Al Majmaah 11952, Saudi Arabia

Mathematics, 2023, vol. 11, issue 15, 1-20

Abstract: A review of the literature demonstrates that the Fox–Wright function is not only a mathematical puzzle, but its role is naturally to represent basic physical phenomena. Motivated by this fact, we studied a new representation of this function in terms of complex delta functions. This representation was useful to compute its Laplace transform with respect to the third parameter γ for which it also generalizes the one and two-parameter Mittag-Leffler functions. New identities involving the Fox–Wright function were discussed and used to simplify the results. Different fractional transforms were evaluated and the solution of a fractional kinetic equation was obtained by using its new representation. Several new properties of this function were discussed as a distribution.

Keywords: Fox–Wright function; Mittag-Leffler function; fractional images; H -function; kinetic equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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