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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Keywords convex function; (s,m)-convex function; Mittag-Leffler function; generalized fractional integral operators

Citation: Ghulam Farid, Saira Bano Akbar, Shafiq Ur Rehman, Josip Pečarić. Boundedness of fractional integral operators containing Mittag-Leffler functions via (s,m)-convexity. AIMS Mathematics, 2020, 5(2): 966-978. doi: 10.3934/math.2020067


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This article has been cited by

  • 1. Xiaoli Qiang, Ghulam Farid, Josip Pečarić, Saira Bano Akbar, Generalized fractional integral inequalities for exponentially (s,m)$(s,m)$-convex functions, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660-020-02335-7
  • 2. Zhihua Chen, Ghulam Farid, Maryam Saddiqa, Saleem Ullah, Naveed Latif, Study of fractional integral inequalities involving Mittag-Leffler functions via convexity, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660-020-02465-y

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