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A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets

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Abstract

This paper improves the modified multiwavelets bases of minimal search method for the fractional integro-differential equation. First, it shows the unique solvability of the equation. And then the Legendre multiwavelets are improved and the modified multiwavelets in reproducing kernel space are obtained. Subsequently, it is established a strict theory for obtaining the \(\varepsilon \)-approximate solution with minimal search method. Finally, some examples show that the modified continuous multiwavelets method is more effective and stable than the Legendre multiwavelets and other methods.

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Acknowledgements

This work is supported by the Natural Science Foundation of Shandong Province of China (No. ZR2020MA050). The authors would like to express their appreciation to the anonymous referees for their many valuable suggestions and for carefully correcting the preliminary version of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, Shandong, People’s Republic of China

    Longbin Wu, Zhong Chen & Xiaohua Ding

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  1. Longbin Wu
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  2. Zhong Chen
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  3. Xiaohua Ding
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Correspondence to Xiaohua Ding.

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Wu, L., Chen, Z. & Ding, X. A minimal search method for solving fractional integro-differential equations based on modified Legendre multiwavelets. J. Appl. Math. Comput. 68, 1467–1483 (2022). https://doi.org/10.1007/s12190-021-01573-2

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