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.
Keywords:differential equations of fractional order, boundary value problem, conformable fractional derivative, artificial neural network, error backpropagation algorithm.
Fulltext:
PDF file (670 kB)