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

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...

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Published inAIMS mathematics Vol. 6; no. 7; pp. 6845 - 6867
Main Authors Zhang, Shuqin, Wang, Jie, Hu, Lei
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
approximate solution
fractional differential equations
initial value problem
variable order caputo fractional derivative
variable order fractional integral
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Abstract 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.
AbstractList 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.
Author Hu, Lei
Zhang, Shuqin
Wang, Jie
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StartPage 6845
SubjectTerms approximate solution
fractional differential equations
initial value problem
variable order caputo fractional derivative
variable order fractional integral
Title On definition of solution of initial value problem for fractional differential equation of variable order
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