Riemann Liouville fractional-like integral operators, convex-like real-valued mappings and their applications over fuzzy domain

Abstract

It is well-known fact that fuzzy number theory is based on the characteristic function but in the fuzzy region, the characteristic function is a membership function that depends upon the interval 01. It means that real numbers and intervals are exceptional cases of fuzzy numbers. By using this approach, another type of Riemann Liouville fractional integral operator has been introduced over a fuzzy domain which is known as Riemann Liouville fractional-like integral operator. These integrals look like Riemann Liouville fractional integral operators but classical integrals are special cases of newly defined integral operators. Some novel versions of these integrals are also obtained and explained by taking the domain's triangular and trapezoidal fuzzy numbers. We also consider the problem of computing scalar-valued. To discuss the application of new integrals, a new class of convex real-valued functions has been introduced, known as convex-like real-valued mappings. With the help of these new concepts, some applications are taken into account. By using convex-like real-valued mappings and newly proposed fractional-like integral operators, the well-known Hermite-Hadamard H.H type and related inequalities are taken into account in this work. Then by defining new differentiable real-valued functions over fuzzy regions, an identity has been obtained and with the support of this identity, certain inequalities are also acquired. Also, we clearly show the important connections of the derived outcomes with those classical integrals. Finally, some nontrivial numerical examples are also provided to verify the correctness of the presented inequalities that occur with the variation of the parameters v and β.