On Equalities for Powers of Singular Differential Operators with Singularity at Zero
DOI:
https://doi.org/10.52575/2687-0959-2026-58-1-29-43Keywords:
Bessel Operator, Hypergeometric Function, Legeandre Function, Taylor FormularAbstract
In the paper we consider explicit realizations in the integral form of fractional powers of Bessel operators. For them connections with Hankel and Mellin transforms and fractional operators are considered. Also Taylor–type formulas are derived with remainder term. The results are important for the theory of partial differential equations, especially with Laplace – Bessel operator.
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Sprinkhuizen-Kuyper IG. A fractional integral operator corresponding to negative powers of a certain second–order differential operator. Journal of Mathematical Analysis and Applications. 1979;72:674–702.
Shishkina E., Sitnik S. Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics. Series: Mathematics in Science and Engineering. 1st Edition. Elsevier. Academic Press; 592 p.
Shishkina EL., Sitnik SM. Fractional Bessel Integrals and Derivatives on Semi-axes. 2020, P. 615–651. In the book: Kravchenko Vladislav, Sitnik Sergei M. (Eds.) Transmutation Operators and Applications. Trends in Mathematics. 2020, Birkhauser Basel, Springer Nature Switzerland AG, Basel.
Shishkina EL., Sitnik SM. On fractional powers of Bessel operators. Journal of Inequalities and Special Functions. (Special issue To honor Prof. Ivan Dimovski’s contributions). 2017;8(1):49–67.
Samko S., Kilbas AA., Marichev OI. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers. Yveron; 1993. 1012 p.
Kilbas AA., Srivastava HM., Truhillo JJ. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam; 2006. 540 p.
Kiryakova V. Generalized Fractional Calculus and Applications.— Pitman Research Notes in Mathematics Series. No. 301. Longman Sci. UK; 1994. 402 p.
Sitnik SM., Shishkina EL. Method of Transmutations for Differential Equations with Bessel operators. Moscow, Fizmatlit; 2019, 224 p.
Katrakhov VV., Sitnik SM. The transmutation method and boundary-value problems for singular elliptic equations. Contemporary Mathematics. Fundamental Directions. 2018;64(2):211–426.
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