Neural Network Method for Solving Time-Fractional Telegraph Equation

Recently, the development of neural network method for solving differential equations has made a remarkable progress for solving fractional differential equations. In this paper, a neural network method is employed to solve time-fractional telegraph equation. The loss function containing initial/boundary conditions with adjustable parameters (weights and biases) is constructed. Also, in this paper, a time-fractional telegraph equation was formulated as an optimization problem. Numerical examples with known analytic solutions including numerical results, their graphs, weights, and biases were also discussed to confirm the accuracy of the method used. Also, the graphical and tabular results were analyzed thoroughly. The mean square errors for different choices of neurons and epochs have been presented in tables along with graphical presentations.

Automated summary

This paper discusses the recent progress in using neural network methods to solve fractional differential equations, particularly focusing on the time-fractional telegraph equation. By constructing a loss function with adjustable parameters and formulating the equation as an optimization problem, the accuracy of the method used was confirmed through numerical examples with known analytic solutions. Thorough analysis of graphical and tabular results, along with presentation of mean square errors for different choices of neurons and epochs, was also conducted.