## Journal of Integral Equations and Applications

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

#### 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

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

#### 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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