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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia

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Volume 19, Issue 3


Integral equations of fractional order in Lebesgue spaces

Nickolai Kosmatov
Published Online: 2016-06-23 | DOI: https://doi.org/10.1515/fca-2016-0035


We discuss solvability of a nonlinear Riemann-Liouville integral equation in Lebesgue spaces. We treat the Volterra equations of the first and the second types by applying boundedness criteria for the Riemann-Liouville integral operator. The existence of a solution to integral equations will follow from the Leray-Schauder Nonlinear Alternative.

Key Words and Phrases: Carathéodory conditions; Leray-Schauder Nonlinear Alternative; Riemann-Liouville derivative; Volterra integral equation

MSC 2010: Primary 34A34; Secondary 34A08; 34A12

Dedicated to Professor Stefan G. Samko on the occasion of his 75th anniversary


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About the article

Received: 2015-08-30

Published Online: 2016-06-23

Published in Print: 2016-06-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 19, Issue 3, Pages 665–675, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2016-0035.

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