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
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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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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