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On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings

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  • Khan, Muhammad Bilal
  • Othman, Hakeem A.
  • Santos-García, Gustavo
  • Saeed, Tareq
  • Soliman, Mohamed S.

Abstract

The most important operator in fractional theory that enables the classical theory of integrals to be generalized is the Riemann-Liouville fractional integrals. In this paper, we have introduced new fractional operators in the fuzzy environment known as fuzzy Riemann-Liouville fractional integrals having exponential kernels. All classical fractional integrals that depend upon exponential kernels are exceptional cases of this new one. Moreover, we have defined a new class of convex mappings which is known as exponential trigonometric convex fuzzy-number valued mappings. With the help of this class and the newly proposed fuzzy fractional integral operator, the well-known Hermite-Hadamard type and related inequalities are taken into account in this work. Moreover, some new versions of midpoint Hermite-Hadamard-type inequalities are also established. By applying these definitions, we have amassed some novel and classical exceptional cases that serve as implementations of the key findings. For the purpose of proving the viability of the fuzzy order relations put forth in this research, some nontrivial examples of fuzzy numbered valued convexity are also provided.

Suggested Citation

  • Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001753
    DOI: 10.1016/j.chaos.2023.113274
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    References listed on IDEAS

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    1. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    2. Khan, Muhammad Bilal & Santos-García, Gustavo & Noor, Muhammad Aslam & Soliman, Mohamed S., 2022. "Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    4. Yongfang Qi & Qingzhi Wen & Guoping Li & Kecheng Xiao & Shan Wang, 2022. "DISCRETE HERMITE–HADAMARD-TYPE INEQUALITIES FOR (s,m)-CONVEX FUNCTION," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-10, November.
    5. Yongfang Qi & Guoping Li & Shan Wang & Qing Zhi Wen, 2022. "Hermite–Hadamard–Fejã‰R-Type Inequalities Via Katugampola Fractional Integrals For S-Convex Functions In The Second Sense," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-11, November.
    6. Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Muhammad Bilal Khan & Ali Althobaiti & Cheng-Chi Lee & Mohamed S. Soliman & Chun-Ta Li, 2023. "Some New Properties of Convex Fuzzy-Number-Valued Mappings on Coordinates Using Up and Down Fuzzy Relations and Related Inequalities," Mathematics, MDPI, vol. 11(13), pages 1-23, June.
    2. Tavazoei, Mohammad Saleh, 2023. "Autonomous second-order nonlinear systems and weighted linearization: Under what conditions are the inherent specifications preserved?," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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