An appropriate fractional Narayana polynomials neural network method for dental caries infection model

Articles in Press

Document Type : Research Article

Authors

Hossein Hassani ¹

Zakieh Avazzadeh ²

Arzu Turan-Dincel ³

Haneyeh Farahmand ⁴

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 Mathematical Engineering, Yildiz Technical University, 34220, Esenler, Istanbul-Turkey

⁴ Department of Oral and Maxillofacial Medicine, School of Dentistry, Yasuj University of Medical Sciences, Yasuj, Iran

10.22067/ijnao.2026.96953.1800

Abstract

Dental caries represents a major global health challenge, affecting individuals of all ages and from various socioeconomic backgrounds. Despite advancements in preventive measures and treatments, it remains the most prevalent chronic disease worldwide, severely impacting both oral and overall health. This condition arises from complex interactions between microorganisms, the host's biological makeup, diet, environmental factors, and behavioral patterns. These factors collectively contribute to the gradual demineralization and breakdown of tooth structures, leading to cavities and tooth decay. To address the mathematical model for simulating the spread of dental caries, a more accurate and effective neural network-based optimization (NNO) technique is suggested. In the present contribution, we introduce new fractional Narayana polynomials (FNPs). The NNO method consists of three main layers which includes an input layer, a hidden layer, and an output layer. Within the structure of the neural network, FNPs are employed as activation functions in the hidden layers, whereas the $arcsinh(t)$ function is utilized for the output layer. The mathematical model for dental caries is reduced to the problem of solving a system of algebraic equations through the use of FNPs, NNO and the Lagrange multipliers method. The convergence analysis, existence and uniqueness of solutions are discussed. The validity of the proposed NNO method is confirmed through relevant simulations. With its high efficiency and accuracy, the proposed NNO method proves to be an effective tool for analyzing the mathematical model for dental caries, showing significant potential for applications in two-dimensional differential equations and optimal control problems.

Keywords

Fractional Narayana polynomials neural network

Dental caries infection model

Optimization algorithm

Lagrange multiplier method

Subjects

• Computational Mathematics

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