Hölder-type spaces, singular operators, and fixed point theorems
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In this paper, continuity and boundedness conditions for linear RiemannLiouville operators and nonlinear Nemytskij operators in Hölder spaces of integral type are studied.Abstract:
In this note, we give a sufficient condition for the existence of Hölder-type solutions to a class of fractional initial value problems involving Caputo derivatives. Since imposing (classical or general) global Lipschitz conditions on the nonlinear operators involved leads to degeneracy phenomena, the main emphasis is put on local Lipschitz conditions or fixed point principles of Schauder and Darbo type. To this end, we study continuity and boundedness conditions for linear RiemannLiouville operators and nonlinear Nemytskij operators in Hölder spaces of integral type which have much better properties than classical Hölder spaces.read more
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Book ChapterDOI
Fixed Point Theory
TL;DR: The first group of results in fixed point theory were derived from Banach's fixed point theorem as discussed by the authors, which is a nice result since it contains only one simple condition on the map F, since it is easy to prove and since it nevertheless allows a variety of applications.
References
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Book ChapterDOI
Fixed Point Theory
TL;DR: The first group of results in fixed point theory were derived from Banach's fixed point theorem as discussed by the authors, which is a nice result since it contains only one simple condition on the map F, since it is easy to prove and since it nevertheless allows a variety of applications.
Book
Measures of Noncompactness and Condensing Operators
TL;DR: Measures of noncompactness as mentioned in this paper are based on linear theory and fixed point index of Condensing Operators (FPO). But they do not consider the non-convexity of the code.
Journal Article
Punti uniti in trasformazioni a codominio non compatto
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.unipd.org/legal. php) of the agreement with the Rendiconti del Seminario Matematico della Università di Padova are discussed.
Journal ArticleDOI
Existence and uniqueness of solutions for a nonlinear fractional initial value problem involving Caputo derivatives
TL;DR: In this article, a sufficient condition for the existence and uniqueness interval of continuous solutions to a class of fractional initial value problems involving Caputo derivatives when the data functions satisfy a non-classical Lipschitz condition was given.