An Artificial Neural Network Approach for Solving Space Fractional Differential Equations

The linear algebraic system generated by the discretization of fractional differential equations has asymmetry, and the numerical solution of this kind of problems is more complex than that of symmetric problems due to the nonlocality of fractional order operators. In this paper, we propose the artificial neural network (ANN) algorithm to approximate the solutions of the fractional differential equations (FDEs). First, we apply truncated series expansion terms to replace unknown function in equations, then we use the neural network to get series coefficients, and the obtained series solution can make the norm value of loss function reach a satisfactory error. In the part of numerical experiments, the results verify that the proposed ANN algorithm can make the numerical results achieve high accuracy and good stability.

Automated summary

This paper proposes an artificial neural network (ANN) algorithm to approximate the solutions of fractional differential equations (FDEs). The algorithm replaces the unknown function in the equations with truncated series expansion terms and uses a neural network to obtain the series coefficients. The resulting series solution achieves a satisfactory error for the norm value of the loss function. Numerical experiments demonstrate that the proposed ANN algorithm can achieve high accuracy and good stability in the numerical results.