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On variational properties of balanced central fractional derivatives
Xu,Yufeng1; Sun,Hai Wei2; Sheng,Qin3
2018-04
Source PublicationInternational Journal of Computer Mathematics
ISSN0020-7160
Volume95Issue:6-7Pages:1195-1209
Abstract

This paper studies variational properties of naturally balanced fractional derivatives based on conventional left-sided and right-sided α-th order formulas, where α ∈ (1/2, 1). Approximations of fractional differential equations equipped with such naturally balanced fractional derivatives are investigated via Ritz–Galerkin approaches. It is found that not only the balanced fractional derivatives possess important variational properties, equations equipped with them exhibit desirable dynamic features as a Ritz–Galerkin formula being applied. Simulation experiments are given to illustrate our conclusions and results.

KeywordFractional Derivatives Fractional Differential Equations Left-sided And Right-sided Formulae Ritz–galerkin Method Variational Principal Weak Solutions
DOI10.1080/00207160.2017.1398324
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000429600100008
PublisherTAYLOR & FRANCIS LTD2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorXu,Yufeng
Affiliation1.Department of Applied MathematicsCentral South University,Changsha,China
2.Department of MathematicsUniversity of Macau,Macao
3.Department of Mathematics and Center for AstrophysicsSpace Physics & Engineering ResearchBaylor University,Waco,United States
Recommended Citation
GB/T 7714
Xu,Yufeng,Sun,Hai Wei,Sheng,Qin. On variational properties of balanced central fractional derivatives[J]. International Journal of Computer Mathematics,2018,95(6-7):1195-1209.
APA Xu,Yufeng,Sun,Hai Wei,&Sheng,Qin.(2018).On variational properties of balanced central fractional derivatives.International Journal of Computer Mathematics,95(6-7),1195-1209.
MLA Xu,Yufeng,et al."On variational properties of balanced central fractional derivatives".International Journal of Computer Mathematics 95.6-7(2018):1195-1209.
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