Optimal solution of kidney function model via fractional clique polynomials neural network

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India.

2 Stony Brook Institute at Anhui University, Anhui University, Hefei 230601, China.

3 Department of Medicine, School of Medicine, Shiraz Nephro-Urology Research Center, Shiraz University of Medical Sciences, Shiraz, Iran.

4 DICEAM Department, Mediterranean University of Reggio Calabria, Via Graziella Feo di Vito, 89060 Reggio Calabria, Italy.

10.22034/cmde.2026.68172.3290

Abstract

We propose the fractional clique polynomials neural network (FCPNN), a hybrid architecture integrating neural networks with fractional clique polynomials (FCPs), to solve mathematical kidney function models (MKFMs) critical for clinical disease modeling. The FCPNN method employs time (in months) as an input variable, with FCPs as activation functions in the hidden layer and the arcsinh(t) function in the output layer, enhancing adaptability to nonlinear biological dynamics. We rigorously establish the method’s theoretical foundations through convergence analysis and proofs of solution existence and uniqueness. By incorporating Lagrange multipliers for optimization, FCPNN improves constraint handling and prediction accuracy. This work advances computational tools for kidney disease modeling, offering a robust framework for personalized medical applications.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 30 April 2026

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History

  • Receive Date: 15 July 2025
  • Revise Date: 03 February 2026
  • Accept Date: 30 April 2026

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