AIMS Mathematics (Oct 2023)

k-Fractional inequalities associated with a generalized convexity

  • Maryam Saddiqa,
  • Saleem Ullah,
  • Ferdous M. O. Tawfiq,
  • Jong-Suk Ro,
  • Ghulam Farid,
  • Saira Zainab

DOI
https://doi.org/10.3934/math.20231460
Journal volume & issue
Vol. 8, no. 12
pp. 28540 – 28557

Abstract

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The aim of this paper is to present the bounds of $ k $-fractional integrals containing the Mittag-Leffler function. For establishing these bounds, a generalized convexity namely strongly exponentially $ (\alpha, h-m)-p $-convexity is utilized. The results of this article provide many new fractional inequalities for several types of fractional integrals and various kinds of convexities. Moreover, an identity is established which helps in proving a Hadamard type inequality.

Keywords