Exponential sampling type neural network Kantorovich operators based on Hadamard fractional integral

This study introduces a novel family of exponential sampling type neural network Kantorovich operators, leveraging Hadamard fractional integrals to significantly enhance function approximation capabilities. By incorporating a flexible parameter alpha, derived from fractional Hadamard integrals, and utilizing exponential sampling, introduced to tackle exponentially sampled data, our operators address critical limitations of existing methods, providing substantial improvements in approximation accuracy. We establish fundamental convergence theorems for continuous functions and demonstrate effectiveness in pth Lebesgue integrable spaces. Approximation degrees are quantified using logarithmic moduli of continuity, asymptotic expansions, and Peetre's K-functional for r-times continuously differentiable functions. A Voronovskaja-type theorem confirms higher-order convergence via linear combinations. Extensions to multivariate cases are proven for convergence in L-p-spaces (1 <= pD1 tunes photosystem II beyond the red-light limit