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Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system

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Abstract

We give an efficient numerical approach to solve variable-order fractional differential equations (VO-FDEs) by applying fractional-order generalized Chelyshkov wavelets (FOGCW). The beta function is used to determine the exact value for the Riemann-Liouville fractional integral operator of the FOGCW. The exact value and the given wavelets are used to solve the VO-FDEs. Six examples are included to demonstrate the effectiveness of this method. In the last example, we show the application of our method to the variable-order fractional relaxation model.

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Acknowledgements

A part of this paper was completed when the corresponding author was working as a researcher at Vietnam Institute for Advance Study in Mathematics (VIASM). The author would like to thank the VIASM for providing a fruitful research environment and extending support and hospitality during their visit. The authors wish to express their sincere thanks to the anonymous referee for valuable suggestions that improved the final version of the manuscript.

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Authors and Affiliations

  1. Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Hoa T. B. Ngo & Thieu N. Vo

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

    Mohsen Razzaghi

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  1. Hoa T. B. Ngo
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  2. Mohsen Razzaghi
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Correspondence to Thieu N. Vo.

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Ngo, H.T.B., Razzaghi, M. & Vo, T.N. Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system. Numer Algor 92, 1571–1588 (2023). https://doi.org/10.1007/s11075-022-01354-3

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