Artificial neural network for solving the nonlinear singular fractional differential equations. Issue 1 (31st December 2023)

• Record Type: Journal Article
• Authors: Althubiti, Saeed; Kumar, Manoj; Goswami, Pranay; Kumar, Kranti
• Is Part Of: Applied mathematics in science and engineering. Volume 31:Issue 1(2023)
• Publication Date: 2023-12-31
• Subjects: MLP neural network -- nonlinear fractional differential equation -- unsupervised learning -- approximate solutions; 41A10 -- 68T07 -- 34K37; Science -- Mathematics -- Periodicals; Engineering mathematics -- Periodicals; Applied mathematics -- Periodicals; 501.51
• DOI: 10.1080/27690911.2023.2187389
• Languages: English
• ISSNs: 2769-0911

Abstract

Abstract : This paper proposes an artificial neural network (ANN) architecture for solving nonlinear fractional differential equations. The proposed ANN algorithm is based on a truncated power series expansion to substitute the unknown functions in the equations in this approach. Then, a set of algebraic equations is resolved using the ANN technique in an iterative minimization process. Finally, numerical examples are provided to demonstrate the usefulness of the ANN architectures. The results verify that the suggested ANN architecture achieves high accuracy and good stability.