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

1
Department of Cognitive Science and Mathematical Modeling, Faculty of Applied Informatics, Wyższa Szkoła Informatyki i Zarządzania, 2 ul. Sucharskiego, 35-225 Rzeszow, Poland
2
Belgorod State National Research University, 85 Pobedy Street, 308015 Belgorod, Russia
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Authors to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1216; https://doi.org/10.3390/math7121216
Received: 20 October 2019 / Revised: 20 November 2019 / Accepted: 24 November 2019 / Published: 10 December 2019
(This article belongs to the Special Issue Direct and Inverse Problems for Fractional Differential Equations)
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. View Full-Text
Keywords: fractional powers of Bessel operator; fractional ODE; Meijer integral transform; Fox–Wright function fractional powers of Bessel operator; fractional ODE; Meijer integral transform; Fox–Wright function
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Shishkina, E.; Sitnik, S. A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type. Mathematics 2019, 7, 1216.

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