Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type

Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type

We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type. The proof of this result is based on a theorem on diffeomorphism...

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Veröffentlicht in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.354-361
Hauptverfasser: Idczak, Dariusz, Walczak, Stanisław, Skowron, Andrzej
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Cauchy problem
Existence theorems
Hilbert space
Integral equations
Mathematical research
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Zusammenfassung:We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type. The proof of this result is based on a theorem on diffeomorphism between Banach and Hilbert spaces. The main assumption is the Palais-Smale condition.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/129478