A Chebyshev neural network-based numerical scheme to solve distributed-order fractional differential equations

Abstract

This study aims to develop a first-order Chebyshev neural network-based technique for solving ordinary and partial distributed-order fractional differential equations. The neural network is used as a trial solution to construct the loss function. The loss function is utilized to train the neural network via an extreme learning machine and obtain the solution. The novelty of this work is developing and implementing a neural network-based framework for distributed-order fractional differential equations via an extreme learning machine. The proposed method is validated on several test problems. The error metrics utilized in the study include the absolute error and the L2 error. A comparison with other previously available approaches is presented. Also, we provide the computation time of the method.