Numerical method for a non-local boundary value problem with Caputo fractional order

Abstract

A non-local boundary value problem with Caputo fractional derivative of order \(1<\nu <2\) is considered in this article. A numerical method comprising of an upwind difference scheme which is used to approximate the convection term and an \(L_2\) approximation of Caputo fractional derivative on an uniform mesh is constructed. Error estimate is derived. Numerical results are presented which validate our numerical method.

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Acknowledgements

The first authour wishes to thank Bharathidasan University for its financial support under URF scheme. The authors wish to thank Department of Science and Technology, Government of India, for the computing facility under DST- PURSE phase II Scheme.

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Correspondence to Ayyadurai Tamilselvan.

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Mary, S.J.C., Tamilselvan, A. Numerical method for a non-local boundary value problem with Caputo fractional order. J. Appl. Math. Comput. (2021). https://doi.org/10.1007/s12190-021-01501-4

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Keywords

  • Fractional differential equation
  • Caputo fractional derivative
  • Non-local boundary value problem
  • Maximum principle
  • Finite difference scheme
  • Error estimate

Mathematics Subject Classification

  • 34A08
  • 26A33
  • 35B50
  • 65L12