Certain Novel Fractional Integral Inequalities via Fuzzy Interval Valued Functions

Abstract

Fuzzy-interval valued functions (FIVFs) are the generalization of interval valued and real valued functions, which have a great contribution to resolve the problems arising in the theory of interval analysis. In this article, we elaborate the convexities and pre-invexities in aspects of FIVFs and investigate the existence of fuzzy fractional integral operators (FFIOs) having a generalized Bessel–Maitland function as their kernel. Using the class of convexities and pre-invexities FIVFs, we prove some Hermite–Hadamard (H-H) and trapezoid-type inequalities by the implementation of FFIOs. Additionally, we obtain other well known inequalities having significant behavior in the field of fuzzy interval analysis.

Keywords

• convex (FIV) function
• fuzzy fractional integral operator
• pre-invex FIV function
• Hermite–Hadamard (H-H)-type inequality
• trapezoid-type inequality
• extended generalized Bessel–Maitland function