Too Much Regularity May Force Too Much Uniqueness

Time-dependent fractional-derivative problems are considered, where is a Caputo fractional derivative of order α ∈ (0, 1)∪(1, 2) and A is a classical elliptic operator, and appropriate boundary and initial conditions are applied. The regularity of solutions to this class of problems is discussed, an...

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Bibliographic Details
Published inFractional calculus & applied analysis Vol. 19; no. 6; pp. 1554 - 1562
Main Author Stynes, Martin
Format Journal Article
LanguageEnglish
Published Warsaw Versita 01.12.2016
De Gruyter
Nature Publishing Group
Subjects
Abstract Harmonic Analysis
Analysis
fractional heat equation
fractional wave equation
Functional Analysis
Initial conditions
Integral Transforms
Mathematics
Operational Calculus
Primary 35R11
Regularity
regularity of solution
Research Paper
Secondary 35B65
Uniqueness
fractional wave equation
regularity of solution
Primary 35R11
fractional heat equation
Secondary 35B65
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Summary:Time-dependent fractional-derivative problems are considered, where is a Caputo fractional derivative of order α ∈ (0, 1)∪(1, 2) and A is a classical elliptic operator, and appropriate boundary and initial conditions are applied. The regularity of solutions to this class of problems is discussed, and it is shown that assuming more regularity than is generally true—as many researchers do—places a surprisingly severe restriction on the problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2016-0080