Estimations of fractional integral operators for convex functions and related results

Abstract

Abstract This research investigates the bounds of fractional integral operators containing an extended generalized Mittag-Leffler function as a kernel via several kinds of convexity. In particular, the established bounds are studied for convex functions and further connected with known results. Furthermore, these results applied to the parabolic function and consequently recurrence relations for Mittag-Leffler functions are obtained. Moreover, some fractional differential equations containing Mittag-Leffler functions are constructed and their solutions are provided by Laplace transform technique.

Keywords

• Convex function
• Mittag-Leffler function
• Generalized fractional integral operators
• Fractional differential equations