University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 2 2026 06 01 An Appropriate Fractional Narayana Polynomials Neural Network Method for a Mathematical Model of the Lung Cancer 217 232 115593 10.22052/ijmc.2026.258001.2093 EN Hossein Hassani Department of Mathematics‎, ‎Anand International College of Engineering‎, ‎Jaipur 303012‎, ‎India Zakieh Avazzadeh Stony Brook Institute at Anhui University‎, ‎Anhui University‎, ‎Hefei 230601‎, ‎China Arzu Turan-Dincel Department of Mathematical Engineering‎, ‎Yildiz Technical University‎, ‎34220‎, ‎Esenler‎, ‎Istanbul-Turkey Ali Bayati Eshkaftaki Faculty of Mathematics‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎Iran Leila Zahiri Department of Internal Medicine‎, ‎Shiraz University of Medical Sciences‎, ‎Shiraz‎, ‎Iran Journal Article 2025 11 21 ‎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. Fractional Narayana polynomials neural network Lung Cancer Cancer cells Immune cells Optimization Algorithm https://ijmc.kashanu.ac.ir/article_115593_830000ec32bfd37942d999b801e84d62.pdf