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

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 ca...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 2; pp. 966 - 978
Main Authors Farid, Ghulam, Bano Akbar, Saira, Ur Rehman, Shafiq, Pečarić, Josip
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
convex function
generalized fractional integral operators
m)-convex function
mittag-leffler function
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020067