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General theory of Caputo-type fractional differential equations

  • This article describes the fundamentals of the theory of ordinary fractional differential equations of Caputo’s type. Starting from the existence and uniqueness of solutions and the well-posedness in general, the flow of topics continues via a derivation of explicit solution formulas for certain important classes of problems and the discussion of their smoothness properties to the stability properties of these solutions. The main focus is on initial value problems, but terminal value problems are briefly considered as well. In addition to dealing with standard single-order problems, the presentation also contains a short discussion of multiterm equations and multiorder systems.

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Metadaten
Author:Kai Diethelm
DOI:https://doi.org/10.1515/9783110571660-001
Parent Title (English):Handbook of Fractional Calculus with Applications, Vol. 2: Fractional Differential Equations
Publisher:De Gruyter
Place of publication:Berlin
Editor:Anatoli Kochubei, Yuri Luchko
Document Type:Part of a Book
Language:English
Year of publication:2019
Release Date:2023/08/10
First Page:1
Last Page:20
Institutes and faculty:Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften
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