Estimations of Bounds on the Multiplicative Fractional Integral Inequalities Having Exponential Kernels

Abstract

To investigate the fractional Hermite–Hadamard-type inequalities, a class of the multiplicative fractional integrals having exponential kernels is introduced. Some estimations of upper bounds for the newly introduced class of integral operators are obtained in terms of the established $^*$differentiable identity. And our results presented in this study are substantial generalizations of previous findings given by Ali et al. (Asian Res J Math 12:1–11, 2019). Three examples are also provided to identify the correctness of the results that occur with the change of the parameter $\alpha $.

Keywords

Hermite–Hadamard-type inequalities / Multiplicative fractional integrals / Multiplicatively convex functions / $^*$Differentiable functions')">$^*$Differentiable functions

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