On the solving fractional Volterra-type differential equations by using artificial neural networks approach

Jafarian A., Rostami F., Khalili Golmankhaneh A.

Progress in Fractional Differentiation and Applications, cilt.5, sa.3, ss.233-242, 2019 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.18576/pfda/050306
  • Dergi Adı: Progress in Fractional Differentiation and Applications
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.233-242
  • Anahtar Kelimeler: Artificial neural networks approach, Back-propagation learning algorithm, Criterion function, Non-linear fractional order Volterra integro-differential equation, Power-series method
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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 backpropagation 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.