Punjab University Journal of Mathematics, Vol 53, No 12 (2021)

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Some new generalizations for exponentially (s; m)-preinvex functions considering generalized fractional integral operators

Farhat Safdar, Muhammad Attique


The generalized fractional integral has been one of the mostuseful operators for modelling non-local behaviors by fractional differentialequations. It is considered, for several integral inequalities by introducingthe concept of exponentially (s;m)-preinvexity. These variantsderived via an extended Mittag-Leffler function based on boundedness,continuity and Hermite-Hadamard type inequalities. The consequencesassociated with fractional integral operators are more general and alsopresent the results for convexity theory. Moreover, we point out that thevariants are useful in solving the problems of science, engineering andtechnology where the Mittag-Leffler function occurs naturally.
AMS (MOS) Subject Classification Codes: 35S29; 40S70; 25U09
KeyWords: Exponentially (s;m)-preinvex functions, Integral inequalities, Mittag-Lefflerfunctions, preinvex functions, convex function..

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