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.
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): | Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International |