An Appropriate Fractional Narayana Polynomials Neural Network Method for a Mathematical Model of the Lung Cancer

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

4 Faculty of Mathematics‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎Iran

5 Department of Internal Medicine‎, ‎Shiraz University of Medical Sciences‎, ‎Shiraz‎, ‎Iran

10.22052/ijmc.2026.258001.2093

Abstract

‎A mathematical model of lung cancer is used to analyze the dynamics of tumor growth and the interactions between cancer cells and immune cells‎. ‎To obtain approximate solutions and improve understanding of the behavior of the state functions‎, ‎a fractional Narayana polynomials neural network (FNPNN) with higher accuracy and better efficiency is proposed‎. ‎For this purpose‎, ‎we develop a method using a three-layer artificial neural network‎, ‎which includes an input layer‎, ‎a hidden layer‎, ‎and an output layer‎. ‎The fractional Narayana polynomials and $arcsinh(t)$ function are utilized as activation functions for the hidden and output layers of the network‎, ‎respectively‎. ‎The lung cancer model is reduced to the problem of solving a system of algebraic equations through the use of FNPNN and the Lagrange multipliers method‎. ‎All computations are performed using Maple and MATLAB software‎. ‎The convergence analysis is discussed‎. ‎The efficiency and versatility of our suggested approach are confirmed by numerical modeling examples‎. ‎The technique proposed in this work can be effortlessly applied to other scientific or engineering problems‎, ‎providing the potential for substantial efficiency gains while keeping accuracy at an acceptable level‎.

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Main Subjects

References

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Iranian Journal of Mathematical Chemistry
Volume 17, Issue 2
June 2026
Pages 217-232

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