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Multi-order fractional differential equations and their numerical solution

  • We consider 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−βn⩽1, βj−βj−1⩽1, 0<β1⩽1, 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.

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Metadaten
Author:Kai Diethelm, Neville J. Ford
URN:urn:nbn:de:bvb:863-opus-20604
DOI:https://doi.org/https://doi.org/10.1016/s0096-3003(03)00739-2
Parent Title (English):Applied Mathematics and Computation
Document Type:Article
Language:English
Year of publication:2004
Publishing Institution:Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt
Release Date:2022/07/20
Volume:154
Issue:3
First Page:621
Last Page:640
Comments:
Accepted version des Artikels
Open access colour:Grün (Zweitveröffentlichung)
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International
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