Estimations of fractional integral operators for convex functions and related results

Advances in Difference Equations

article

Chen, Zhihua¹  Farid, Ghulam²  Ur Rehman, Atiq²  Latif, Naveed³ 

[1] Institute of Computing Science and Technology, Guangzhou University;Department of Mathematics, COMSATS University Islamabad;General Studies Department, Jubail Industrial College

关键词: Convex function;    Mittag-Leffler function;    Generalized fractional integral operators;    Fractional differential equations;   

DOI  :  10.1186/s13662-020-02621-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY