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Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus

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  • Muhammad Bilal Khan

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan)

  • Gustavo Santos-García

    (Facultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain)

  • Hatim Ghazi Zaini

    (Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Savin Treanță

    (Department of Applied Mathematics, Politehnica University of Bucharest, 060042 Bucharest, Romania)

  • Mohamed S. Soliman

    (Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

Abstract

In interval analysis, the fuzzy inclusion relation and the fuzzy order relation are two different concepts. Under the inclusion connection, convexity and non-convexity form a substantial link with various types of inequalities. Moreover, convex fuzzy-interval-valued functions are well known in convex theory because they allow us to infer more exact inequalities than convex functions. Most likely, integral operators play significant roles to define different types of inequalities. In this paper, we have successfully introduced the Riemann–Liouville fractional integrals on coordinates via fuzzy-interval-valued functions (FIVFs). Then, with the help of these integrals, some fuzzy fractional Hermite–Hadamard-type integral inequalities are also derived for the introduced coordinated convex FIVFs via a fuzzy order relation (FOR). This FOR is defined by φ -cuts or level-wise by using the Kulish–Miranker order relation. Moreover, some related fuzzy fractional Hermite–Hadamard-type integral inequalities are also obtained for the product of two coordinated convex fuzzy-interval-valued functions. The main results of this paper are the generalization of several known results.

Suggested Citation

  • Muhammad Bilal Khan & Gustavo Santos-García & Hatim Ghazi Zaini & Savin Treanță & Mohamed S. Soliman, 2022. "Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:534-:d:745071
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    References listed on IDEAS

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    1. Mihai, Marcela V. & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some integral inequalities for harmonic h-convex functions involving hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 257-262.
    2. Yanrong An & Guoju Ye & Dafang Zhao & Wei Liu, 2019. "Hermite-Hadamard Type Inequalities for Interval ( h 1 , h 2 )-Convex Functions," Mathematics, MDPI, vol. 7(5), pages 1-9, May.
    3. Chen, Feixiang, 2015. "Extensions of the Hermite–Hadamard inequality for harmonically convex functions via fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 121-128.
    4. Hongxin Bai & Muhammad Shoaib Saleem & Waqas Nazeer & Muhammad Sajid Zahoor & Taiyin Zhao & Viliam Makis, 2020. "Hermite-Hadamard- and Jensen-Type Inequalities for Interval h1,h2 Nonconvex Function," Journal of Mathematics, Hindawi, vol. 2020, pages 1-6, April.
    5. Fangfang Shi & Guoju Ye & Dafang Zhao & Wei Liu, 2020. "Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    6. Feixiang Chen & Shanhe Wu, 2014. "Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, August.
    7. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    8. Muhammad Aslam Noor & Khalida Inayat Noor & Michael Th. Rassias, 2021. "Characterizations of Higher Order Strongly Generalized Convex Functions," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 341-364, Springer.
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    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.

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