On two classes of operators of generalized fractional integro-differentiation

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.