Solution of fractional order diffusion equations with clique neural network

Authors

Merve Zeynep Kaya, Distance Education Center, Agri Ibrahim Cecen University, Agri, TürkiyeFollow
Mesut Karabacak, Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, TürkiyeFollow
Ercan Çelik, Department of Applied Mathematics and Informatics, Faculty of Science, Kyrgyz-Turkish Manas University, Bishkek, KyrgyzstanFollow

Abstract

In this paper, the clique artificial neural network method is used to solve the fractional diffusion equation, which is a subclass of partial differential equations. The clique neural network architecture is constructed using input, hidden, and output layers. Several degrees of clique polynomials were used as activation functions, and the output layer was obtained by multiplying them with weight coefficients. Subsequently, the optimization equation was derived, and the exact solution, numerical solution, and error function graphs were obtained using a specialized algorithm. Analysis of the results demonstrates that the clique artificial neural network method provides quicker and more accurate results compared to previously studied methods.

Recommended Citation

Kaya, Merve Zeynep; Karabacak, Mesut; and Çelik, Ercan (2025) "Solution of fractional order diffusion equations with clique neural network," Mathematical Modelling and Numerical Simulation with Applications: Vol. 5: Iss. 3, Article 4.
DOI: https://doi.org/10.53391/2791-8564.1003
Available at: https://mmnsa.researchcommons.org/journal/vol5/iss3/4