文章基本信息

标题：Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations
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作者：Naveed Ahmad Khan ; Osamah Ibrahim Khalaf ; Carlos Andrés Tavera Romero 等
期刊名称：Computational Intelligence and Neuroscience
印刷版ISSN：1687-5265
电子版ISSN：1687-5273
出版年度：2022
卷号：2022
DOI：10.1155/2022/2710576
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this study, the intelligent computational strength of neural networks (NNs) based on the backpropagated Levenberg-Marquardt (BLM) algorithm is utilized to investigate the numerical solution of nonlinear multiorder fractional differential equations (FDEs). The reference data set for the design of the BLM-NN algorithm for different examples of FDEs are generated by using the exact solutions. To obtain the numerical solutions, multiple operations based on training, validation, and testing on the reference data set are carried out by the design scheme for various orders of FDEs. The approximate solutions by the BLM-NN algorithm are compared with analytical solutions and performance based on mean square error (MSE), error histogram (EH), regression, and curve fitting. This further validates the accuracy, robustness, and efficiency of the proposed algorithm.