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

Muhammad Bilal Khan, Gustavo Santos-García, Hatim Ghazi Zaini, Savin Treanță and Mohamed S. Soliman
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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

Mathematics, 2022, vol. 10, issue 4, 1-26

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.

Keywords: fuzzy Riemann–Liouville fractional integrals; Hermite–Hadamard-type inequality; fuzzy-interval-valued functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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