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Fractional Calculus and Applied Analysis

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LP-solutions for fractional integral equations

1COMSATS Institute of Information Technology, M. A. Jinnah Building, Ali Akbar Road, Lahore, Pakistan

2Abdus Salam School of Mathematical Sciences, GC University, 68-B New Muslim Town, Lahore, Pakistan

3Constantin Brancusi University, Republicii 1, 210152, Targu-Jiu, Romania

4School of Mathematics, Statistics and Applied Mathematics National University of Ireland, University Road, Galway, Ireland

© 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Fractional Calculus and Applied Analysis. Volume 17, Issue 1, Pages 259–276, ISSN (Online) 1314-2224, DOI: 10.2478/s13540-014-0166-4, December 2013

Publication History

Published Online:
2013-12-28

Abstract

In this article, we examine L p-solutions of fractional integral equations in Banach spaces involving the Riemann-Liouville integral operator. Using a compactness type condition, we obtain local and global existence of solutions. Also other types of existence and uniqueness results are established. At the end, an application is given to illustrate the main result.

MSC: Primary 26A33; Secondary 34A07, 47H08, 35A01

Keywords: fractional integral equations; Lp-solutions; measure of noncompactness; existence and uniqueness results

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