Journal of Integral Equations and Applications

Solvability and uniform local attractivity for a Volterra equation of convolution type

Luciano Abadias, Edgardo Alvarez, Józef Banaś, and Carlos Lizama

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Abstract

We show the existence of uniformly locally attractive solutions for a nonlinear Volterra integral equation of convolution type with a general kernel. We use methods and techniques of fixed point theorems and properties of measure of noncompactness. We extend earlier results obtained in the context of integral equations of fractional order. We give new insights about a new and striking relation between the size of data and the fractional order $\alpha >0$ of the kernel $k(t)=t^{\alpha -1}/\Gamma (\alpha )$.

Article information

Source
J. Integral Equations Applications, Volume 31, Number 2 (2019), 149-164.

Dates
First available in Project Euclid: 23 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1569225671

Digital Object Identifier
doi:10.1216/JIE-2019-31-2-149

Mathematical Reviews number (MathSciNet)
MR4010582

Zentralblatt MATH identifier
07118799

Subjects
Primary: 45D05: Volterra integral equations [See also 34A12]
Secondary: 47H08: Measures of noncompactness and condensing mappings, K-set contractions, etc. 34A08: Fractional differential equations

Keywords
Nonlinear Volterra integral equation fixed-point theorem measure of noncompactness uniformly locally attractive solution

Citation

Abadias, Luciano; Alvarez, Edgardo; Banaś, Józef; Lizama, Carlos. Solvability and uniform local attractivity for a Volterra equation of convolution type. J. Integral Equations Applications 31 (2019), no. 2, 149--164. doi:10.1216/JIE-2019-31-2-149. https://projecteuclid.org/euclid.jiea/1569225671


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