Research on New Interval-Valued Fractional Integrals with Exponential Kernel and Their Applications

This paper aims to introduce a new fractional extension of the interval Hermite–Hadamard (HH), HH–Fejér, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings (LRIVH convex mappings) with an exponential function in the kernel. We use fractional operators to develop several generalizations, capturing unique outcomes that are currently under investigation, while also introducing a new operator. Generally, we propose two methods that, in conjunction with more generalized fractional integral operators with an exponential function in the kernel, can address certain novel generalizations of increasing mappings under the assumption of LRIV convexity, yielding some noteworthy results. The results produced by applying the suggested scheme show that the computational effects are extremely accurate, flexible, efficient, and simple to implement in order to explore the path of upcoming intricate waveform and circuit theory research.