"On the Solving Fractional Volterra-Type Differential Equations by Usin" by Ahmad Jafarian, Fariba Rostami et al.

Progress in Fractional Differentiation & Applications

Article Title

On the Solving Fractional Volterra-Type Differential Equations by Using Artificial Neural Networks Approach

Authors

Ahmad Jafarian, Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, IranFollow
Fariba Rostami
Alireza Khalili Golmankhaneh

Author Country (or Countries)

Iran

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/050306

Recommended Citation

Jafarian, Ahmad; Rostami, Fariba; and Khalili Golmankhaneh, Alireza (2019) "On the Solving Fractional Volterra-Type Differential Equations by Using Artificial Neural Networks Approach," Progress in Fractional Differentiation & Applications: Vol. 5: Iss. 3, Article 6.
DOI: http://dx.doi.org/10.18576/pfda/050306
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol5/iss3/6

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