The Numerical Solution of Nonlinear Fractional Lienard and Duffing Equations Using Orthogonal Perceptron

Autor:	Akanksha Verma, Wojciech Sumelka, Pramod Kumar Yadav
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	orthogonal neural network simulated annealing optimization technique fractional differential equations Caputo derivative Mathematics QA1-939
Zdroj:	Symmetry, Vol 15, Iss 9, p 1753 (2023)
Druh dokumentu:	article
ISSN:	2073-8994
DOI:	10.3390/sym15091753
Popis:	This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing equations with a Caputo fractional derivative. These equations show the oscillating circuit and generalize the spring–mass device equation. The proposed approach transforms the given nonlinear fractional differential equation (FDE) into an unconstrained minimization problem. The simulated annealing (SA) algorithm minimizes the mean square error. The proposed techniques examine various non-integer order problems to verify the theoretical results. The numerical results show that the proposed approach yields better results than existing methods.
Databáze:	Directory of Open Access Journals
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