Extended ‎A‎artificial Neural Networks Approach and Fractional Volterra ‎I‎ntegro-Differential Equation‎s

The current research intends to apply an extended version of arti cial neural networks approach for solving a linear fractional Volterra integro-dierential equation. More precisely, our main discussion in this study is to answer this fundamental question practically: That is, would it be possible to speed up the convergence of a given neural network structure by substituting the standard rst-order derivative with a fractional order one. It is worth mentioning that, there is no certain geometric interpretation for fractional order derivative of a continuous function at a point in the domain. But, we strongly believe that this derivative calculus might help us to discover an ecient iterative technique to approximate solution of the earlier mentioned math problem. In this way, two simple but typical comparative test problems are given, and the related salient features of this technique are also discussed.