Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

In this work, a methodology based on a neural network to solve fractal-fractional differential equations with a nonsingular and nonlocal kernel is proposed, the neural network is optimized by the Levenberg–Marquardt algorithm. For evaluating the neural network, different chaotic oscillators of varia...

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Bibliographic Details
Published inEngineering with computers Vol. 38; no. 3; pp. 2669 - 2682
Main Authors Zúñiga-Aguilar, C. J., Gómez-Aguilar, J. F., Romero-Ugalde, H. M., Escobar-Jiménez, R. F., Fernández-Anaya, G., Alsaadi, Fawaz E.
Format Journal Article
LanguageEnglish
Published London Springer London 01.06.2022
Springer Nature B.V
Subjects
Algorithms
Approximation
Artificial neural networks
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Differential equations
Fractals
Fractional calculus
Information technology
Math. Applications in Chemistry
Mathematical analysis
Mathematical and Computational Engineering
Neural networks
Original Article
Oscillators
Systems Theory
Fractal-fractional definition
Nonlinear fractional differential equations
Fractional calculus
Variable-order fractal-fractional derivative
Artificial neural networks
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Summary:In this work, a methodology based on a neural network to solve fractal-fractional differential equations with a nonsingular and nonlocal kernel is proposed, the neural network is optimized by the Levenberg–Marquardt algorithm. For evaluating the neural network, different chaotic oscillators of variable order are solved and compared with algorithms of numeric approximation.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-020-01229-y