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AIMS Mathematics

2021, Volume 6, Issue 7: 6845-6867. doi: 10.3934/math.2021401
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Research article

On definition of solution of initial value problem for fractional differential equation of variable order

  • 1.
    Department of Mathematics, China University of Mining and Technology Beijing, Beijing 100083, China
  • 2.
    School of Science, Shandong Jiaotong University, Jinan, 250357, China
  • Received: 27 December 2020 Accepted: 13 April 2021 Published: 22 April 2021

  • MSC : 26A33

  • We propose a new definition of continuous approximate solution to initial value problem for differential equations involving variable order Caputo fractional derivative based on the classical definition of solution of integer order (or constant fractional order) differential equation. Some examples are presented to illustrate these theoretical results.

    Citation: Shuqin Zhang, Jie Wang, Lei Hu. On definition of solution of initial value problem for fractional differential equation of variable order[J]. AIMS Mathematics, 2021, 6(7): 6845-6867. doi: 10.3934/math.2021401

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  • We propose a new definition of continuous approximate solution to initial value problem for differential equations involving variable order Caputo fractional derivative based on the classical definition of solution of integer order (or constant fractional order) differential equation. Some examples are presented to illustrate these theoretical results.




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