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Artificial neural network approach for a class of fractional ordinary differential equation

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Abstract

The essential characteristic of artificial neural networks which against the logistic traditional systems is a data-based approach and has led a number of higher education scholars to investigate its efficacy, during the past few decades. The aim of this paper was concerned with the application of neural networks to approximate series solutions of a class of initial value ordinary differential equations of fractional orders, over a bounded domain. The proposed technique uses a suitable truncated power series of the solution function and transforms the original differential equation in a minimization problem. Then, the minimization problem is solved using an accurate neural network model to compute the parameters with high accuracy. Numerical results are given to validate the iterative method.

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Authors and Affiliations

  1. Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran

    Ahmad Jafarian & Masoumeh Mokhtarpour

  2. Department of Mathematics, Cankaya University, Eskisehir Yolu 29 km, 06810, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Ahmad Jafarian
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  2. Masoumeh Mokhtarpour
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  3. Dumitru Baleanu
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Correspondence to Dumitru Baleanu.

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Jafarian, A., Mokhtarpour, M. & Baleanu, D. Artificial neural network approach for a class of fractional ordinary differential equation. Neural Comput & Applic 28, 765–773 (2017). https://doi.org/10.1007/s00521-015-2104-8

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  • DOI: https://doi.org/10.1007/s00521-015-2104-8

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