On the Composition Structures of Certain Fractional Integral Operators

Abstract

This paper investigates the composition structures of certain fractional integral operators whose kernels are certain types of generalized hypergeometric functions. It is shown how composition formulas of these operators can be closely related to the various Erdélyi-type hypergeometric integrals. We also derive a derivative formula for the fractional integral operator and some applications of the operator are considered for a certain Volterra-type integral equation, which provide two generalizations to Khudozhnikov’s integral equation (see below). Some specific relationships, examples, and some future research problems are also discussed.

Keywords

• composition operators
• Erdélyi-type integral
• fractional integral operator
• generalized hypergeometric function