On boundedness of fractional integral operators via several kinds of convex functions

Abstract

For generalizations of concepts of different fields fractional derivative operators as well as fractional integral operators are useful notions. Our aim in this paper is to discuss boundedness of the integral operators which contain Mittag-Leffler function in their kernels. The results are obtained for strongly (α,h−m)-convex functions which hold for different kinds of convex functions at the same time. They also give improvements/refinements of many already published results.

Keywords

• strongly (α，h−m)-convex function
• generalized fractional integral operators
• unified mittag-leffler function
• bounds