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An investigation of radial basis functions for fractional derivatives and their applications

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Abstract

In the present study, the radial basis functions (RBF) are combined with polynomial basis functions to approximate the fractional derivatives specifically. We explore two new types of local support fields for the first time in the literature. In addition, we apply the RBF, combined with an appropriate number of polynomial basis functions featuring a new type of local support field to solve the single-term, multi-term ordinary fractional equations, time–space and two-side space fractional partial differential equations. Finally, the accuracy of the presented method is demonstrated via numerical experiments.

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Acknowledgements

The project was partially supported by the Fundamental Research Funds for the Central Universities (Nos. 20720180003 and 20720160002). The authors also wish to acknowledge that this research was partially supported by the Australian Research Council via the Discovery Projects (Nos. DP180103858 and DP190101889) and the National Natural Science Foundation of China (Nos. 11772046, 11701467 and 11771364).

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Qingxia Liu & Pinghui Zhuang

  2. Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen, 361005, People’s Republic of China

    Qingxia Liu & Pinghui Zhuang

  3. School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia

    Fawang Liu

  4. College of Mathematics and Data Science, Minjiang University, Fuzhou, 350108, People’s Republic of China

    Junjiang Lai

  5. Faculty of Science, Engineering and Technology, Swinburne University of Technology, PO Box 218, Hawthorn, VIC, 3122, Australia

    Vo Anh

  6. School of Economic Mathematics Swufe, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Shanzhen Chen

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  1. Qingxia Liu
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  2. Pinghui Zhuang
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  3. Fawang Liu
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  4. Junjiang Lai
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  5. Vo Anh
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  6. Shanzhen Chen
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Correspondence to Pinghui Zhuang.

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Liu, Q., Zhuang, P., Liu, F. et al. An investigation of radial basis functions for fractional derivatives and their applications. Comput Mech 65, 475–486 (2020). https://doi.org/10.1007/s00466-019-01779-z

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  • DOI: https://doi.org/10.1007/s00466-019-01779-z

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