Progress in Fractional Differentiation & Applications

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Lately, there is a great concern in the applications of the artificial neural networks approach in modeling and mathematically analyze various complex real-world phenomena. In this literature, one of the most successful and effective neural network architectures has been implemented to construct the numerical solution of the fractional Volterra-type equations. For this aim, one supervised back- propagation type learning algorithm which is planned on a three-layered feed-forward neural network is applied for approximating the mentioned problem as a convergent power series solution. To be more precise, we have also considered some numerical examples with the comparison to the results given by the Euler wavelet method. Obtained simulation and numerical results illustrate that the proposed iterative technique is globally convergent and specially efficient for solving this fractional problem.

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