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

• Published in: Chaos, solitons and fractals solitons and fractals, 2023-04, Vol.169, p.113274, Article 113274
• Main Authors: Khan, Muhammad Bilal, Othman, Hakeem A., Santos-García, Gustavo, Saeed, Tareq, Soliman, Mohamed S.
• Format: Article
• Language: English
• Subjects: Exponential trigonometric convex fuzzy-number valued mappings (exponential trigonometric F·N-V·M); Fuzzy Riemann-Liouville fractional integral operators; Hermite-Hadamard inequalities; Midpoint Hermite-Hadamard inequalities
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2023.113274

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. •In this paper, we have introduced new fractional operators in the fuzzy environment which are 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.•We know that, in the fields of applied mathematics and engineering, the theory of convex mapping has several uses. Therefore, 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 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 version of midpoint Hermite-Hadamard type inequalities are also established.•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.