Novel fractional inequalities measured by Prabhakar fuzzy fractional operators pertaining to fuzzy convexities and preinvexities

Iqra Nayab; Shahid Mubeen; Rana Safdar Ali; Faisal Zahoor; Muath Awadalla; Abd Elmotaleb A. M. A. Elamin; Iqra Nayab; Shahid Mubeen; Rana Safdar Ali; Faisal Zahoor; Muath Awadalla; Abd Elmotaleb A. M. A. Elamin

doi:10.3934/math.2024860

AIMS Mathematics

2024, Volume 9, Issue 7: 17696-17715. doi: 10.3934/math.2024860

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Research article

Novel fractional inequalities measured by Prabhakar fuzzy fractional operators pertaining to fuzzy convexities and preinvexities

1.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
2.
Department of Mathematics, University of Lahore, Lahore, Pakistan
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia
4.
Department of Mathematics, College of Science and Humanity, Prince Sattam bin Abdulaziz University, Sulail, Al-Kharj 11942, Saudi Arabia

Received: 21 February 2024 Revised: 03 May 2024 Accepted: 13 May 2024 Published: 22 May 2024
MSC : 05A30, 26D10, 26D15

In this article, we implemented the idea of a fuzzy interval-valued function with the well-known generalized fuzzy fractional operators, associated with different types of convexities and preinvexities. We developed the Prabhakar fuzzy fractional operators using the fuzzy interval-valued function. We presented the novel extensions of Hermite-Hadamard fuzzy-type and trapezoidal fuzzy-type inequalities, based on the $ h $-Godunova-Levin convex and $ h $-Godunova preinvex fuzzy interval-valued functions.
- fuzzy fractional integral,
- fuzzy interval-valued function,
- preinvex function,
- fuzzy convexity,
- Hermite-Hadamard inequality
Citation: Iqra Nayab, Shahid Mubeen, Rana Safdar Ali, Faisal Zahoor, Muath Awadalla, Abd Elmotaleb A. M. A. Elamin. Novel fractional inequalities measured by Prabhakar fuzzy fractional operators pertaining to fuzzy convexities and preinvexities[J]. AIMS Mathematics, 2024, 9(7): 17696-17715. doi: 10.3934/math.2024860

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Abstract

In this article, we implemented the idea of a fuzzy interval-valued function with the well-known generalized fuzzy fractional operators, associated with different types of convexities and preinvexities. We developed the Prabhakar fuzzy fractional operators using the fuzzy interval-valued function. We presented the novel extensions of Hermite-Hadamard fuzzy-type and trapezoidal fuzzy-type inequalities, based on the $ h $-Godunova-Levin convex and $ h $-Godunova preinvex fuzzy interval-valued functions.

References

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