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The key purpose of this study is to suggest a new fractional extension of Hermite–Hadamard, Hermite–Hadamard–Fejér and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.

Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems