Multi-order fractional differential equations and their numerical solution

Hdl Handle:
http://hdl.handle.net/10034/69499
Title:
Multi-order fractional differential equations and their numerical solution
Authors:
Diethelm, Kai; Ford, Neville J.
Abstract:
This article considers the numerical solution of (possibly nonlinear) fractional differential equations of the form y(α)(t)=f(t,y(t),y(β1)(t),y(β2)(t),…,y(βn)(t)) with α>βn>βn−1>>β1 and α−βn1, βj−βj−11, 0<β11, combined with suitable initial conditions. The derivatives are understood in the Caputo sense. We begin by discussing the analytical questions of existence and uniqueness of solutions, and we investigate how the solutions depend on the given data. Moreover we propose convergent and stable numerical methods for such initial value problems.
Affiliation:
Technische Universität Braunschweig ; University College Chester
Citation:
Applied Mathematics and Computation, 154(3), 2004, pp. 621-640
Publisher:
Elsevier
Journal:
Applied Mathematics and Computation
Publication Date:
2004
URI:
http://hdl.handle.net/10034/69499
DOI:
10.1016/S0096-3003(03)00739-2
Additional Links:
http://www.elsevier.com/wps/find/journaldescription.cws_home/522482/description#description
Type:
Article
Language:
en
Description:
This article is not available through ChesterRep.
ISSN:
0096-3003
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorDiethelm, Kaien
dc.contributor.authorFord, Neville J.en
dc.date.accessioned2009-06-01T12:01:50Zen
dc.date.available2009-06-01T12:01:50Zen
dc.date.issued2004en
dc.identifier.citationApplied Mathematics and Computation, 154(3), 2004, pp. 621-640en
dc.identifier.issn0096-3003en
dc.identifier.doi10.1016/S0096-3003(03)00739-2en
dc.identifier.urihttp://hdl.handle.net/10034/69499en
dc.descriptionThis article is not available through ChesterRep.en
dc.description.abstractThis article considers the numerical solution of (possibly nonlinear) fractional differential equations of the form y(α)(t)=f(t,y(t),y(β1)(t),y(β2)(t),…,y(βn)(t)) with α>βn>βn−1>>β1 and α−βn1, βj−βj−11, 0<β11, combined with suitable initial conditions. The derivatives are understood in the Caputo sense. We begin by discussing the analytical questions of existence and uniqueness of solutions, and we investigate how the solutions depend on the given data. Moreover we propose convergent and stable numerical methods for such initial value problems.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://www.elsevier.com/wps/find/journaldescription.cws_home/522482/description#descriptionen
dc.subjectmulti-term fractional differential equationen
dc.subjectCaputo derivativeen
dc.subjectexistenceen
dc.subjectuniquenessen
dc.subjectstructural stabilityen
dc.subjectAdams methoden
dc.titleMulti-order fractional differential equations and their numerical solutionen
dc.typeArticleen
dc.contributor.departmentTechnische Universität Braunschweig ; University College Chesteren
dc.identifier.journalApplied Mathematics and Computationen
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