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A new numerical method for solving semilinear fractional differential equation

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Abstract

The fractional differential equation has been used to describe many phenomenons in almost all applied sciences, such as fluid flow in porous materials, anomalous diffusion transport, acoustic wave propagation in viscoelastic materials, and others. In some cases, it is complicated to find the analytical solution of a fractional differential equation, so there are some special techniques to approximate the solution. In this paper, a new collocation method for a class of semilinear fractional differential equations has been constructed. The convergence properties of the proposed methods and the computational complexity are treated. Some numerical experiments are presented to validate the theoretical results. The proposed numerical method provides an alternative way to study some physical phenomena by fractional differential equations.

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Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities (Grant Number: 2572020BC06).

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Authors and Affiliations

  1. College of Science, Heilongjiang Bayi Agricultural University, Daqing, 163319, China

    Yufen Wei

  2. Institute of Cold Regions Science and Engineering, Northeast Forestry University, Harbin, 150040, China

    Ying Guo & Yu Li

  3. Department of Mathematics, Northeast Forestry University, Harbin, 150040, China

    Yu Li

Authors
  1. Yufen Wei
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  2. Ying Guo
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  3. Yu Li
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Correspondence to Yu Li.

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Wei, Y., Guo, Y. & Li, Y. A new numerical method for solving semilinear fractional differential equation. J. Appl. Math. Comput. 68, 1289–1311 (2022). https://doi.org/10.1007/s12190-021-01566-1

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  • DOI: https://doi.org/10.1007/s12190-021-01566-1

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