DOI: https://doi.org/10.26089/NumMet.v26r317

Neural network method for solving boundary value problems for fractional order differential equations

Authors

  • Tien Duc Nguyen

Keywords:

differential equations of fractional order
boundary value problem
conformable fractional derivative
artificial neural network
error backpropagation algorithm

Abstract

Many problems in physics, mechanics and other sciences are related to solving boundary value problems for fractional differential equations. Finding exact solutions to these problems is very difficult, and in this case, we have to look for approximate solutions. This paper proposes a mathematical method for approximate solving of a boundary value problems for fractional differential equations. For fractional derivatives we use the definition of a conformable fractional derivative. We use a feedforward neural network model with one hidden layer. The model is trained in a supervised learning mode using the backpropagation algorithm to optimize the error function and update the neural network parameters. To illustrate our method, a computer program was developed to conduct experiments in which the obtained results are compared with analytical solutions.


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Published

2025-07-11

Issue

Vol. 26 (2025): Issue 3.

Section

Methods and algorithms of computational mathematics and their applications

Author

Tien Duc Nguyen

Kazan Federal University,
Institute of Computational Mathematics and Information Technologies
• PhD Student

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