Abstract
In this paper we introduce fractional quasi-Bessel equations
and construct their existence theory in the class of fractional series solutions. In order to find the parameters of the series, we derive the characteristic equation, which is surprisingly independent of the terms with non-matching parameters \(\xi _i\ne \alpha _i\). Our methodology allows us to obtain new results for a broad class of fractional differential equations including quasi-Euler equations. As a particular example, we demonstrate how our approach works for the constant-coefficient equations. The theoretical results are justified computationally.
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Acknowledgements
The authors would like to thank Professor Boyadjiev for drawing our attention to the fractional Bessel equation. Also, the authors are obliged to Professor Kiryakova and the Reviewers for the valuable recommendations.
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Dubovski, P.B., Slepoi, J.A. Construction and analysis of series solutions for fractional quasi-Bessel equations. Fract Calc Appl Anal 25, 1229–1249 (2022). https://doi.org/10.1007/s13540-022-00045-z
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DOI: https://doi.org/10.1007/s13540-022-00045-z
Keywords
- Fractional differential equations
- Fractional calculus
- Mittag-Leffler functions
- Quasi-Bessel equations
- Fractional power series
- Existence
- Cauchy-Euler equations
- Quasi-Euler equations
- Constant-coefficient equations
- Blow-up of solutions