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Fractional-Lucas optimization method for evaluating the approximate solution of the multi-dimensional fractional differential equations

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Abstract

The paper investigates the numerical solution of the multi-dimensional fractional differential equations by applying fractional-Lucas functions (FLFs) and an optimization method. First, the FLFs and their properties are introduced. Then, according to the pseudo-operational matrix of derivative and modified operational matrix of fractional derivative, we present the framework of numerical technique. Also, for computational technique, we evaluate the upper bound of error. As a result, we expound the proposed scheme by solving several kinds of problems. Our computational results demonstrate that the proposed method is powerful and applicable for nonlinear multi-order fractional differential equations, time-fractional convection–diffusion equations with variable coefficients, and time-space fractional diffusion equations with variable coefficients.

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Acknowledgements

We express our sincere thanks to the anonymous referees for valuable suggestions that improved the final manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical sciences, Alzahra University, Tehran, Iran

    Haniye Dehestani & Yadollah Ordokhani

  2. Department of Mathematics and Statistics, Mississippi State University, Starkville, MS, 39762, USA

    Mohsen Razzaghi

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  1. Haniye Dehestani
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  2. Yadollah Ordokhani
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Correspondence to Yadollah Ordokhani.

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Dehestani, H., Ordokhani, Y. & Razzaghi, M. Fractional-Lucas optimization method for evaluating the approximate solution of the multi-dimensional fractional differential equations. Engineering with Computers 38, 481–495 (2022). https://doi.org/10.1007/s00366-020-01048-1

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