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A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense

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Abstract

This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help explain a variety of real-world physical problems. The technique implemented in this paper converts the original differential equation into a minimization problem using a suggested truncated power series of the solution function. Next, answer to the problem is obtained via computing the parameters with highly precise neural network model. We can get a good approximate solution of FFDEs by combining the initial conditions with the ANNs performance. Examples are provided to portray the efficiency and applicability of this method. Comparison with similar existing approaches are also conducted to demonstrate the accuracy of the proposed approach.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Universiti Putra Malaysia, Serdang, Selangor, Malaysia

    A. M. Shloof & N. Senu

  2. Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor, Malaysia

    N. Senu

  3. Department of Mathematics, Faculty of Science, Al-Zintan University, Alzintan, Libya

    A. M. Shloof

  4. Department of Law, Economics and Human Sciences, Mediterranea University of Reggio Calabria, Reggio Calabria, Italy

    A. Ahmadian

  5. Department of Mathematics, Near East University, TRNC, Mersin 10, Nicosia, Turkey

    A. Ahmadian

  6. Atmospheric Science and Meteorological Research Center (ASMERC), Climatological Research Institute (CRI), Mashhad, Iran

    M. Pakdaman

  7. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    S. Salahshour

Authors
  1. A. M. Shloof
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  2. N. Senu
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  3. A. Ahmadian
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  4. M. Pakdaman
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  5. S. Salahshour
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Corresponding authors

Correspondence to N. Senu or A. Ahmadian.

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Shloof, A.M., Senu, N., Ahmadian, A. et al. A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense. Engineering with Computers 39, 505–515 (2023). https://doi.org/10.1007/s00366-022-01607-8

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  • DOI: https://doi.org/10.1007/s00366-022-01607-8

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