$ k $-Fractional inequalities associated with a generalized convexity

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

doi:10.3934/math.20231460

AIMS Mathematics

2023, Volume 8, Issue 12: 28540-28557. doi: 10.3934/math.20231460

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Research article

$ k $-Fractional inequalities associated with a generalized convexity

1.
Department of Mathematics, Air University Islamabad, Pakistan
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
3.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
4.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
5.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
6.
School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan

Received: 31 July 2023 Revised: 28 September 2023 Accepted: 10 October 2023 Published: 19 October 2023
MSC : 26A33, 26A51, 33E12

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.
- convex function,
- strongly exponentially $ (\alpha, h-m)-p $-convex function,
- Mittag-Leffler function,
- generalized fractional integrals
Citation: Maryam Saddiqa, Saleem Ullah, Ferdous M. O. Tawfiq, Jong-Suk Ro, Ghulam Farid, Saira Zainab. $ k $-Fractional inequalities associated with a generalized convexity[J]. AIMS Mathematics, 2023, 8(12): 28540-28557. doi: 10.3934/math.20231460

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Abstract

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.

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