Mathematical modeling demonstrates generalized p-convex inequalities within fractal fractional calculus, highlighting exceptional accuracy via neural network verification.
In this article, we developed a new variant of discrete Jensen-type inequality for p-convex functions over fractal sets. Improvement and generalization of some Jensen-Mercer-type estimates for [Formula: see text]-convex function in the framework of fractal fractional calculus are obtained. Using this Jensen-Mercer inequality, we establish a Hermite-Hadamard-Mercer (HHM) type inequalities for [Formula: see text]-convex functions in fractal dimensions. We drive a new integral identity and HHM type inequalities for differentiable [Formula: see text]-convex functions. Some of the results presented here for [Formula: see text]-convex functions are extensions of earlier results for harmonically convex and convex functions. Finally, we also provide a neural network-based numerical analysis of the obtained results, showing the accuracy and effectiveness of the proposed inequalities for [Formula: see text]-convex functions.
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Butt et al. (2026) studied this question.
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