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

  • Qingxia Liu
  • Pinghui ZhuangEmail author
  • Fawang Liu
  • Junjiang Lai
  • Vo Anh
  • Shanzhen Chen
Original Paper
  • 30 Downloads

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.

Keywords

Fractional derivatives Mixed RBF Local support fields Polynomial basis functions Jacobi–Gauss–Lobatto quadratures 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Qingxia Liu
    • 1
    • 2
  • Pinghui Zhuang
    • 1
    • 2
    Email author
  • Fawang Liu
    • 3
  • Junjiang Lai
    • 4
  • Vo Anh
    • 5
  • Shanzhen Chen
    • 6
  1. 1.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputationXiamen UniversityXiamenPeople’s Republic of China
  3. 3.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia
  4. 4.College of Mathematics and Data ScienceMinjiang UniversityFuzhouPeople’s Republic of China
  5. 5.Faculty of Science, Engineering and TechnologySwinburne University of TechnologyHawthornAustralia
  6. 6.School of Economic Mathematics SwufeSouthwestern University of Finance and EconomicsChengduPeople’s Republic of China

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