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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Elina Shishkina & Sergey Sitnik, 2019. "A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1216-:d:296314
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    Citations

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    Cited by:

    1. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2024. "Time–space fractional Euler–Poisson–Darboux equation with Bessel fractional derivative in infinite and finite domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 383-402.
    2. Azamat Dzarakhohov & Yuri Luchko & Elina Shishkina, 2021. "Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator," Mathematics, MDPI, vol. 9(13), pages 1-18, June.

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