Modeling the propagation of fractional inequalities via generalized fractional operators with artificial neural networks

This paper examines the generalized reverse forms of well-known Minkowski, Hölder and Hermite-Hadamard (HH)-Fejér inequalities within an interval-valued (ι.υ)(⋋₁^q₁+1,℧) class of convexity by deploying the generalized k-Prabhakar fractional integral operator (FIO). Our findings exhibit wide relevance by adjusting parameter bounds for generalized k-Prabhakar FIO within the structure of ι.υ(⋋₁^q₁+1,℧) class of convexity resulting in novel improvements to inequalities. These inequalities are computed graphically and tabularly to obtain a visualization of the inequalities. The results emphasize the importance of mathematical inequalities in solving optimization problems. Furthermore, an artificial neural network (ANN) model is utilized to provide predictions of the left, middle and right sides of the inequalities. The predictions of the ANNs show a close agreement with the theoretical results and therefore validate the strength of the proposed methodology. By integrating deep learning, this approach demonstrates the predictive capability of the inequalities over a broad parameter range.