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Title: Hölder-type spaces, singular operators, and fixed point theorems
Authors: Appell, J.
Dutkiewicz, A.
López Brito, María Belén 
Reinwand, S.
Sadarangani Sadarangani, Kishin Bhagwands 
UNESCO Clasification: 120219 Ecuaciones diferenciales ordinarias
Keywords: Initial value problem
Caputo derivative
Singular integral equation
Riemann-Liouville operator
Nemytskij operator, et al
Issue Date: 2021
Journal: Fixed Point Theory 
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 Riemann-Liouville operators and nonlinear Nemytskij operators in Hölder spaces of integral type which have much better properties than classical Hölder spaces.
ISSN: 1583-5022
DOI: 10.24193/fpt-ro.2021.1.03
Source: Fixed Point Theory, v. 22 (1), p. 31-58, (2021)
Appears in Collections:Artículos
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