A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type

Elina Shishkina and Sergey Sitnik
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Elina Shishkina: Department of Cognitive Science and Mathematical Modeling, Faculty of Applied Informatics, Wyższa Szkoła Informatyki i Zarządzania, 2 ul. Sucharskiego, 35-225 Rzeszow, Poland
Sergey Sitnik: Belgorod State National Research University, 85 Pobedy Street, 308015 Belgorod, Russia

Mathematics, 2019, vol. 7, issue 12, 1-21

Abstract: In this article we propose and study a method to solve ordinary differential equations with left-sided fractional Bessel derivatives on semi-axes of Gerasimov–Caputo type. We derive explicit solutions to equations with fractional powers of the Bessel operator using the Meijer integral transform.

Keywords: fractional powers of Bessel operator; fractional ODE; Meijer integral transform; Fox–Wright function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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