An Application of ANNs Method for Solving Fractional Fredholm Equations

Abstract

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. 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.

A Novel Approach for the Solution of a Class of Urysohn Integrale Quations Using Bernstein Polynomials.

“…The general form of the Bernstein polynomials [13][14][15][16] of nth degree over the interval [ , ] is defined by…”