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A Meshless Method for the Numerical Solution of Fractional Stochastic Integro-Differential Equations Based on the Moving Least Square Approach

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Abstract

Recently, more and more researchers focus on stochastic fractional equations due to their applicability to describe the memory and randomness of many noise systems problems. In the current work, we develop a meshless approach based on moving least square approximation (MLS) to solve stochastic fractional integro-differential equations (SFIDEs). To establish the scheme; we consider the composite Gauss-Legendre integration rule for computing the singular-fractional integral and the Riemann sum for estimating It\(\hat{o}\) integral. We have also compared different basis in terms of CPU time. The error bound of the method is provided. The major accuracy of this approach is that the approximate solutions converge more quickly to the exact solutions by choosing a small number of basis functions and nodes, then the computational cost of the moment matrix is reduced. Several numerical test problems are presented. Comparing the results obtained with other methods confirm the efficiency of the proposed scheme.

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Acknowledgements

The authors sincerely thank the referees for providing them suggestions and constructive comments which led to the improvement of this article.

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There was no funding support for the work reported in the paper.

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Authors and Affiliations

  1. MISI Laboratory, Hassan First University, Settat, Morocco

    Zahra El Majouti & Rachid El Jid

  2. Department of Mathematics, University of Mazandran, P.O. Box 47415-95447, Babolsar, Iran

    Elham Taghizadeh

Authors
  1. Zahra El Majouti
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  2. Elham Taghizadeh
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  3. Rachid El Jid
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El Majouti, Z., Taghizadeh, E. & El Jid, R. A Meshless Method for the Numerical Solution of Fractional Stochastic Integro-Differential Equations Based on the Moving Least Square Approach. Int. J. Appl. Comput. Math 9, 27 (2023). https://doi.org/10.1007/s40819-023-01521-7

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