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Zeitschrift für Analysis und ihre Anwendungen


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Volume 33, Issue 1, 2014, pp. 65–85
DOI: 10.4171/ZAA/1499

Published online: 2013-12-27

Solvability of Fractional Integral Equations on an Unbounded Interval through the Theory of Volterra-Stieltjes Integral Equations

Tomasz Zając[1]

(1) Rzeszów University of Technology, Poland

In this paper we study the existence of solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous and bounded on the interval of nonnegative numbers. Moreover, we also investigate the solvability of the equation in question in the classes of functions being asymptotically stable or having limits at infinity, for example. The main tool used in our considerations is the technique of measures of noncompactness constructed in a special way. It is shown that results obtained in the paper are applicable to the class of fractional integral equations and Volterra-Chandrasekhar integral equations, among others.

Keywords: Function of bounded variation, Riemann-Stieltjes integral, measure of noncompactness, fractional integral equation, Volterra-Stieltjes integral equation, attractivity, asymptotic stability

Zając Tomasz: Solvability of Fractional Integral Equations on an Unbounded Interval through the Theory of Volterra-Stieltjes Integral Equations. Z. Anal. Anwend. 33 (2014), 65-85. doi: 10.4171/ZAA/1499