A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type
Abstract
:1. Introduction
2. Basic Definitions
2.1. Special Functions
2.2. Integral Transforms and Transmutation Poisson Operator
3. Left-Sided Fractional Bessel Integral and Derivative on Semi-Axes
3.1. Definitions of Left-Sided Fractional Bessel Integral and Derivative on Semi-Axes
3.2. Meijer Transform of Left-Sided Fractional Bessel Integral and Derivative on Semi-Axes
4. Meijer Transform Method for Solution to Homogeneous Fractional Equation with the Left-Sided Fractional Bessel Derivatives on Semi-Axes of Gerasimov–Caputo Type
4.1. General Case
4.2. Particular Cases and Examples
5. Conclusions
Author Contributions
Conflicts of Interest
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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. https://doi.org/10.3390/math7121216
Shishkina E, Sitnik S. A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type. Mathematics. 2019; 7(12):1216. https://doi.org/10.3390/math7121216
Chicago/Turabian StyleShishkina, Elina, and Sergey Sitnik. 2019. "A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type" Mathematics 7, no. 12: 1216. https://doi.org/10.3390/math7121216
APA StyleShishkina, E., & Sitnik, S. (2019). A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type. Mathematics, 7(12), 1216. https://doi.org/10.3390/math7121216