Existence and uniqueness for a class of iterative fractional differential equations

Existence and uniqueness for a class of iterative fractional differential equations

The presence of a self-mapping increases the difficulty in proving the existence and uniqueness of solutions for general iterative fractional differential equations. In this article, we provide conditions for the existence and uniqueness of solutions for the initial value problem. We also determine...

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Veröffentlicht in:Advances in difference equations 2015-03, Vol.2015 (1), p.1-13, Article 78
Hauptverfasser: Ibrahim, Rabha W, Kılıçman, Adem, Damag, Faten H
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Difference and Functional Equations
Difference equations
Differential equations
Functional Analysis
Initial value problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Recent Progress in Differential and Difference Equations
Stability
Uniqueness
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Beschreibung
Zusammenfassung:The presence of a self-mapping increases the difficulty in proving the existence and uniqueness of solutions for general iterative fractional differential equations. In this article, we provide conditions for the existence and uniqueness of solutions for the initial value problem. We also determine the Burton stability of such equations. The arbitrary order case is taken in the sense of Riemann-Liouville fractional operators.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-015-0421-y