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Numerical solution of variable order fractional differential equations by using shifted Legendre cardinal functions and Ritz method

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Abstract

In this paper, we present a new numerical method for solving variable order fractional differential equations, which is based on shifted Legendre cardinal functions. First, we obtain the pseudo-operational matrix of the variable order fractional derivative by applying the properties mentioned in the Caputo derivative of fractional variable order. Then, using Ritz method, the pseudo-operational matrix and collocation method, the problem is reduced to a system of algebraic equations that is solved by Newton’s iterative method. Illustrative examples are included to demonstrate the efficiency and accuracy of the proposed method.

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Acknowledgements

We would like to thank the referees for their valuable comments and helpful suggestions to improve the earlier version of this paper.

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Authors and Affiliations

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

    Faezeh Sadat Yousefi & Yadollah Ordokhani

  2. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    Sohrabali Yousefi

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  1. Faezeh Sadat Yousefi
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  2. Yadollah Ordokhani
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  3. Sohrabali Yousefi
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Correspondence to Yadollah Ordokhani.

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Yousefi, F.S., Ordokhani, Y. & Yousefi, S. Numerical solution of variable order fractional differential equations by using shifted Legendre cardinal functions and Ritz method. Engineering with Computers 38, 1977–1984 (2022). https://doi.org/10.1007/s00366-020-01192-8

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  • DOI: https://doi.org/10.1007/s00366-020-01192-8

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