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BOUNDARY VALUE METHODS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

Yongtao Zhou1,2, Chengjian Zhang1,2, Huiru Wang1,2   

  1. 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
    2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2018-11-12 Revised:2019-06-03 Online:2021-01-15 Published:2021-03-11
  • Supported by:
    The authors would like to thank the anonymous referees for their valuable comments and helpful suggestions. The second author Chengjian Zhang (corresponding author) is supported by NSFC (Grant No. 11971010).

Yongtao Zhou, Chengjian Zhang, Huiru Wang. BOUNDARY VALUE METHODS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Computational Mathematics, 2021, 39(1): 108-129.

This paper deals with the numerical computation and analysis for Caputo fractional differential equations (CFDEs). By combining the p-order boundary value methods (BVMs) and the m-th Lagrange interpolation, a type of extended BVMs for the CFDEs with γ-order (0 < γ < 1) Caputo derivatives are derived. The local stability, unique solvability and convergence of the methods are studied. It is proved under the suitable conditions that the convergence order of the numerical solutions can arrive at min {p, m-γ + 1}. In the end, by performing several numerical examples, the computational efficiency, accuracy and comparability of the methods are further illustrated.

CLC Number: 

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