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

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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Main Authors: Shuqin Zhang, Jie Wang, Lei Hu
Format: Article
Language:English
Published: AIMS Press 2021-04-01
Series:AIMS Mathematics
Subjects:
variable order caputo fractional derivative
variable order fractional integral
fractional differential equations
initial value problem
approximate solution
Online Access:http://www.aimspress.com/article/doi/10.3934/math.2021401?viewType=HTML
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spelling doaj-8add89e5a9ec4f47a2dfed1cba9e0b752021-04-27T01:08:57ZengAIMS PressAIMS Mathematics2473-69882021-04-01676845686710.3934/math.2021401On definition of solution of initial value problem for fractional differential equation of variable orderShuqin Zhang0Jie Wang 1Lei Hu 21. Department of Mathematics, China University of Mining and Technology Beijing, Beijing 100083, China1. Department of Mathematics, China University of Mining and Technology Beijing, Beijing 100083, China2. School of Science, Shandong Jiaotong University, Jinan, 250357, ChinaWe 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.http://www.aimspress.com/article/doi/10.3934/math.2021401?viewType=HTMLvariable order caputo fractional derivativevariable order fractional integralfractional differential equationsinitial value problemapproximate solution
collection DOAJ
language English
format Article
sources DOAJ
author Shuqin Zhang
Jie Wang
Lei Hu
spellingShingle Shuqin Zhang
Jie Wang
Lei Hu
On definition of solution of initial value problem for fractional differential equation of variable order
AIMS Mathematics
variable order caputo fractional derivative
variable order fractional integral
fractional differential equations
initial value problem
approximate solution
author_facet Shuqin Zhang
Jie Wang
Lei Hu
author_sort Shuqin Zhang
title On definition of solution of initial value problem for fractional differential equation of variable order
title_short On definition of solution of initial value problem for fractional differential equation of variable order
title_full On definition of solution of initial value problem for fractional differential equation of variable order
title_fullStr On definition of solution of initial value problem for fractional differential equation of variable order
title_full_unstemmed On definition of solution of initial value problem for fractional differential equation of variable order
title_sort on definition of solution of initial value problem for fractional differential equation of variable order
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2021-04-01
description 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.
topic variable order caputo fractional derivative
variable order fractional integral
fractional differential equations
initial value problem
approximate solution
url http://www.aimspress.com/article/doi/10.3934/math.2021401?viewType=HTML
work_keys_str_mv AT shuqinzhang ondefinitionofsolutionofinitialvalueproblemforfractionaldifferentialequationofvariableorder
AT jiewang ondefinitionofsolutionofinitialvalueproblemforfractionaldifferentialequationofvariableorder
AT leihu ondefinitionofsolutionofinitialvalueproblemforfractionaldifferentialequationofvariableorder
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