AIMS Mathematics, 2020, 5(2): 966-978. doi: 10.3934/math.2020067

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

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

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.
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