Extended artificial neural networks approach for solving two-dimensional fractional-order Volterra-type integro-differential equations

Abstract

Over the years, there has been a sharp increase in employing artificial neural networks in modeling and simulation of complicated real-world problems. The main aim of the present paper is to apply an extension of artificial neural networks approach for approximating solution of a two-dimensional fractional-order linear Volterra-type integro-differential initial value problem. For this aim, a suitable four-layered feed forward neural architecture is designed to approximate the solution function with the help of two distinct famous learning algorithms, namely the steepest descent and the quasi-Newton rules, to any desired degree of accuracy. Finally, the applicability and validity of preset techniques are described and tested through some numerical examples. Numerical and simulation results obtained here are also compared with the results obtained by the optimal Homotopy asymptotic method. This practice determined that the quasi-Newton rule provides far more accurate solutions than the other two mentioned above.