Numerical solution of Bagley-Torvik equations using Legendre artificial neural network method

In this article, we have used the Legendre artificial neural network to find the solution of the Bagley-Torvik equation, which is a fractional-order ordinary differential equation. Caputo fractional derivative has been considered throughout the presented work to handle the fractional order differential equation. The training of optimal weights of the network has been carried out using a simulated annealing optimization technique. Here we have presented three examples to exhibit the precision and relevance of the proposed technique with comparison to the other numerical methods with error analysis. The proposed technique is an easy, highly efficient, and robust technique for finding the approximate solution of fractional-order ordinary differential equations.