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Weighted bounded solutions for a class of nonlinear fractional equations.

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Abstract

Let T be a bounded linear operator defined on a Banach space X. We investigate the existence of solutions for a class of nonlinear fractional equation in the form

$$\left( * \right)\left\{ \begin{array}{l} {\Delta ^\alpha }Uu\left( n \right) = Tu\left( n \right) + f,\,\,\left( {n,u\left( n \right)} \right)\,,\,n \in {N_0},0 \alpha \le 1; \\ u\left( 0 \right) = x, \\ \end{array} \right.$$

on the vector-valued weighted sequence space

$$l_f^\infty \left( {N;X} \right) = \left\{ {x:N \to X/\begin{array}{*{20}{c}} {\sup } \\ {n \in N} \\ \end{array}\frac{{\left\| {x\left( n \right)} \right\|}}{{nn!}} \infty } \right\}.$$

Our analysis relies on the fixed point theory and operator-theoretical methods.

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Authors and Affiliations

  1. Facultad de Ciencias Departamento de Matemáticas y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile

    Carlos Lizama

  2. Universidad Politécnica de Madrid Escuela Técnica Superior de Ingeniería y Sistemas de Telecomunicación, Ctra. de Valencia, Km 7, 28030, Madrid, Spain

    M. Pilar Velasco

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  1. Carlos Lizama
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  2. M. Pilar Velasco
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Correspondence to Carlos Lizama.

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Lizama, C., Velasco, M.P. Weighted bounded solutions for a class of nonlinear fractional equations.. FCAA 19, 1010–1030 (2016). https://doi.org/10.1515/fca-2016-0055

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