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Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities

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  • Khan, Muhammad Bilal
  • Santos-García, Gustavo
  • Noor, Muhammad Aslam
  • Soliman, Mohamed S.

Abstract

The theory of convex mapping has a lot of applications in the field of applied mathematics and engineering. The fuzzy Riemann-Liouville fractional integrals are the most significant operator of fractional theory which permits to generalize the classical theory of integrals. This study considers the well-known Hermite-Hadamard type and associated inequalities. To full fill this mileage, some new versions of fuzzy Hermite-Hadamard type and Hermite-Hadamard-Fejér type inequalities for up and down convex fuzzy-number valued mappings have been obtained. Some new related fuzzy Hermite-Hadamard type inequalities are also obtained with the help of product of two up and down convex fuzzy-number valued mappings. Moreover, we have introduced some new important classes of fuzzy numbered valued convexity which are known as lower up and down convex (concave) and, upper up and down convex (concave) fuzzy numbered valued mappings by applying some mild restrictions on up and down convex (concave) fuzzy numbered valued mappings. By using these definitions, we have acquired many classical and new exceptional cases which can be viewed as applications of the main results. We also present three examples of fuzzy numbered valued convexity to demonstrate the validity of the fuzzy inclusion relations proposed in this paper.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008712
    DOI: 10.1016/j.chaos.2022.112692
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    References listed on IDEAS

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    1. Singh, D. & Dar, B.A. & Kim, D.S., 2016. "KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions," European Journal of Operational Research, Elsevier, vol. 254(1), pages 29-39.
    2. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
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    Cited by:

    1. Muhammad Bilal Khan & Eze R. Nwaeze & Cheng-Chi Lee & Hatim Ghazi Zaini & Der-Chyuan Lou & Khalil Hadi Hakami, 2023. "Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates," Mathematics, MDPI, vol. 11(24), pages 1-27, December.
    2. 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.
    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. Tareq Saeed & Muhammad Bilal Khan & Savin Treanță & Hamed H. Alsulami & Mohammed Sh. Alhodaly, 2023. "Study of Log Convex Mappings in Fuzzy Aunnam Calculus via Fuzzy Inclusion Relation over Fuzzy-Number Space," Mathematics, MDPI, vol. 11(9), pages 1-16, April.
    5. 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).
    6. Eghlimi, Hadi & Asgari, Mohammad Sadegh, 2023. "A study of the time-fractional heat equation under the generalized Hukuhara conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Muhammad Bilal Khan & Hakeem A. Othman & Aleksandr Rakhmangulov & Mohamed S. Soliman & Alia M. Alzubaidi, 2023. "Discussion on Fuzzy Integral Inequalities via Aumann Integrable Convex Fuzzy-Number Valued Mappings over Fuzzy Inclusion Relation," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    8. Khan, Muhammad Bilal & Guirao, Juan L.G., 2023. "Riemann Liouville fractional-like integral operators, convex-like real-valued mappings and their applications over fuzzy domain," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    9. 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.
    10. Muhammad Bilal Khan & Aleksandr Rakhmangulov & Najla Aloraini & Muhammad Aslam Noor & Mohamed S. Soliman, 2023. "Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    11. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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