An investigation of incomplete H−functions associated with some fractional integral operators

Abstract

Arbitrary-order integral operators find variety of implementations in different science disciplines as well as engineering fields. The study presented as part of this research paper derives motivation from the fact that applications of fractional operators and special functions demonstrate a huge potential in understanding many of physical phenomena. Study and investigation of a fractional integral operator containing an incomplete H? functions (IHFs) as the kernel is the primary objective of the research work presented here. Specifically, few interesting relations involving the new fractional operator with IHFs in its kernel and classical Riemann Liouville(R-L) fractional integral and derivative operators, the Hilfer fractional derivative operator, the generalized composite fractonal derivate operaor are established. Results established by the authors in [1-3] follow as few interesting and significant special cases of our main results.