AN APPLICATION OF ANNS ON POWER SERIES METHOD FOR SOLVING FRACTIONAL FREDHOLM TYPE INTEGRO-DIFFERENTIAL EQUATIONS

摘要

For the last decade, several authors demonstrated the performance of artificial neural network models over other traditional testing methods. The current research, aimed to present a global optimization technique based on combination of neural networks approach and power series method for the numerical solution of a fractional Fredholm type integro-differential equation involving the Caputo derivative. The mentioned problem to be solved approximately for the unknown series coefficients via a three-layer feed-forward neural architecture. In other words, an accurate truncated power series representation of the solution function is achieved when a suitable learning algorithm is used for the suggested neural architecture. As applications of the present iterative approach, some kinds of integro-differential equations are investigated. The achieved simulations are compared with the results obtained by some existing algorithms.