Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator

Azamat Dzarakhohov, Yuri Luchko and Elina Shishkina
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Azamat Dzarakhohov: Department of Mathematics and Physics, Gorsky State Agrarian University, Kirov Str. 37, North Ossetia-Alania, 362040 Vladikavkaz, Russia
Yuri Luchko: Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany
Elina Shishkina: Department of Mathematical and Applied Analysis, Voronezh State University, Universitetskaya pl., 1, 394018 Voronezh, Russia

Mathematics, 2021, vol. 9, issue 13, 1-18

Abstract: In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral transform and its modification, fundamental solutions to these equations are derived in terms of the Fox–Wright function, the Fox H-function, and their particular cases. We also provide some explicit formulas for the solutions to the corresponding initial-value problems in terms of the generalized convolutions introduced in this paper.

Keywords: Fox–Wright function; H-function; fractional powers of the Bessel operator; fractional Euler–Poisson–Darboux equation; fractional ODE; Meijer integral transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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