Boundedness of fractional integral operators containing Mittag-Leffler functions via (s,m)-convexity

AIMS Mathematics

Shafiq Ur Rehman¹  Ghulam Farid¹  Saira Bano Akbar²  Josip Pečarić³ 

[1] 1 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan;2 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan;3 Rudn University, Moscow, Russia;

关键词: convex function;    (s;    m)-convex function;    mittag-leffler function;    generalized fractional integral operators;   

DOI  :  10.3934/math.2020067

来源: DOAJ

【 摘 要 】

The objective of this paper is to derive the bounds of fractional integral operators which contain Mittag-Leffler functions in the kernels. By using (s,m)-convex functions bounds of these operators are evaluated which lead to obtain their boundedness and continuity. Moreover the presented results can be used to get various results for known fractional integrals and functions deducible from (s,m)-convexity. Also a version of Hadamard type inequality is established for (s,m)-convex functions via generalized fractional integrals.

【 授权许可】

Unknown