Geodesic
On two classes of operators of generalized fractional integro-differentiation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 109-122

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The paper is a survey of two special classes of generalized fractional integro-differentiation operators studied earlier in detail by the authors; all results are presented without proofs. A list of various fractional integro-differentiation operators with brief historical background is given. Further, we discuss main results of the theory of Bushman–Erdélyi operators. This class includes the classical Riemann–Liouville and Erdélyi–Kober operators, the Mehler–Fock transformation, transformation operators for the singular Bessel operator, and others. Also, we present main results for operators of fractional Bessel integro-differentiation.
Keywords: fractional integro-differentiation, Riemann–Liouville operator, Erdélyi–Kober operator, transformation operator, Buschman–Erdélyi operator, fractional power of Bessel operators. 
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     author = {S. M. Sitnik and E. L. Shishkina},
     title = {On two classes of operators of generalized fractional integro-differentiation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {109--122},
     publisher = {mathdoc},
     volume = {198},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_198_a12/}
}
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S. M. Sitnik; E. L. Shishkina. On two classes of operators of generalized fractional integro-differentiation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 109-122. http://geodesic.mathdoc.fr/item/INTO_2021_198_a12/