2013
DOI: 10.2478/s13540-013-0037-4
|View full text |Cite
|
Sign up to set email alerts
|

Waveform relaxation methods for fractional functional differential equations

Abstract: In this paper, we use waveform relaxation method to solve fractional functional differential equations. Under suitable conditions imposed on the so-called splitting functions the convergence results of the waveform relaxation method are given. Delay dependent error estimates for the method are derived. Error bounds for some special cases are considered. Numerical examples illustrate the feasibility and efficiency of the method. It is the first time for applying the method in the fractional functional different… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3

Citation Types

0
3
0

Year Published

2014
2014
2020
2020

Publication Types

Select...
6

Relationship

2
4

Authors

Journals

citations
Cited by 9 publications
(3 citation statements)
references
References 32 publications
0
3
0
Order By: Relevance
“…On the other hand, it can also decouple a complicated differential system into a set of simplified subsystems. Some authors have successfully applied the WR method into solving ordinary differential equations [12][13][14][15], differential-algebraic equations [16], functional differential equations [17] and fractional differential equations [18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, it can also decouple a complicated differential system into a set of simplified subsystems. Some authors have successfully applied the WR method into solving ordinary differential equations [12][13][14][15], differential-algebraic equations [16], functional differential equations [17] and fractional differential equations [18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…[20], the WR method is used to solve linear and nonlinear time-fractional ODEs, and proper convergent splitting is constructed. Then, the WR method is extended to handle fractional DDEs [21] and DAEs [22]. In ref.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional order differential systems arise from many branches of applied mathematics and physics, such as gas dynamics, Newtonian fluid mechanics, nuclear physics, and biological process [1][2][3][4][5][6][7][8][9][10][11][12]. In the recent years, there has a significant development in fractional calculus.…”
Section: Introductionmentioning
confidence: 99%