A survey on impulsive fractional differential equations

Recently, in series of papers we have proposed different concepts of solutions of impulsive fractional differential equations (IFDE). This paper is a survey of our main results about IFDE. We present several types of such equations with various boundary value conditions as well. Concept of solutions...

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Bibliographic Details
Published inFractional calculus & applied analysis Vol. 19; no. 4; pp. 806 - 831
Main Authors Wang, JinRong, Fečkan, Michal
Format Journal Article
LanguageEnglish
Published Warsaw Versita 01.08.2016
De Gruyter
Nature Publishing Group
Subjects
34A08
34K37
35R11
Abstract Harmonic Analysis
Analysis
Boundary value problems
Differential equations
fractional calculus
fractional ordinary and partial differential equations
Functional Analysis
Integral Transforms
Mathematical analysis
Mathematics
Mittag-Leffler type functions
noninstantaneous impulsive fractional differential equations
nonlocal impulsive fractional switched systems
Operational Calculus
Primary 26A33
Secondary 33E12
Survey Paper
fractional calculus
Primary 26A33
noninstantaneous impulsive fractional differential equations
35R11
Mittag-Leffler type functions
Secondary 33E12
34K37
fractional ordinary and partial differential equations
34A08
nonlocal impulsive fractional switched systems
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Summary:Recently, in series of papers we have proposed different concepts of solutions of impulsive fractional differential equations (IFDE). This paper is a survey of our main results about IFDE. We present several types of such equations with various boundary value conditions as well. Concept of solutions, existence results and examples are presented. Proofs are only sketched.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2016-0044