Jump to ContentJump to Main Navigation

Fractional Calculus and Applied Analysis

6 Issues per year

Impact Factor 2014: 2.245
Rank 11 out of 310 in category Mathematics, 12 out of 255 in Applied Mathematics and 14 out of 99 in Mathematics, Interdisciplinary Applications in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR): 2.106
Source Normalized Impact per Paper (SNIP): 2.079

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:


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

  • [1] R.P. Agarwal, S. Arshad, D. O’Regan, V. Lupulescu, Fuzzy fractional integral equations under compactness type condition. Fract. Calc. and Appl. Anal. 15, No 4 (2012), 572–590; DOI: 10.2478/s13540-012-0040-1; http://link.springer.com/article/10.2478/s13540-012-0040-1. [CrossRef]

  • [2] A. Aghajani, E. Pourhadi, J.J. Trujillo, Application of measure of noncompactness to a cauchy problem for fractional differential equations in banach spaces. Fract. Calc. and Appl. Anal. 16, No 4 (2013), 962–977; DOI: 0.2478/s13540-013-0059-y; http://link.springer.com/article/10.2478/s13540-013-0059-y.

  • [3] T.A. Barton, I.K. Purnaras, L p-solutions of singular integro-differential equations. J. Math. Anal. Appl., 386 (2012), 830–841. http://dx.doi.org/10.1016/j.jmaa.2011.08.041 [CrossRef]

  • [4] T.A. Barton, B. Zhang, L p-solutions of fractional differential equations. Nonlinear Studies 19, No 2 (2012), 161–177.

  • [5] K. Diethelm, The Analysis of Fractional Differential Equations. Springer, 2004.

  • [6] D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces. Ser. Mathematics and its Applications, Vol. 373, Kluwer Academic Publishers, Dordrecht-Boston-London, 1996. http://dx.doi.org/10.1007/978-1-4613-1281-9 [CrossRef]

  • [7] L. Kexue, P. Jigen, G. Jinghuai, Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness. Fract. Calc. and Appl. Anal. 15, No 4 (2012), 591–610; DOI: 10.2478/s13540-012-0041-0; http://link.springer.com/article/10.2478/s13540-012-0041-0. [CrossRef]

  • [8] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, Vol. 204, Elsevier, New York, 2006. http://dx.doi.org/10.1016/S0304-0208(06)80001-0 [CrossRef]

  • [9] C. Kuratowski, Sur les espaces complets. Fundamenta Mathematica 51 (1930), 301–309.

  • [10] V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge, 2009.

  • [11] D. Mamrilla, On L p-solutions of nth order nonlinear differential equations. Časopis pro pěstování matematiky 113 (1988), 363–368.

  • [12] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1993.

  • [13] K.B. Oldham, J. Spanier, The Fractional Calculus. Academic Press, New York, 1974.

  • [14] I. Podlubny, Fractional Differential Equations. Academic Press, San Diego, 1999.

  • [15] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Sci. Publishers, London-New York 1993.

  • [16] H.A.H. Salem, M. Väth, An abstract Gronwall lemma and application to global existence results for functional differential and integral equations of fractional order. J. of Integral Equations and Applications 16, No 4 (2004), 441–439. http://dx.doi.org/10.1216/jiea/1181075299 [CrossRef]

Comments (0)

Please log in or register to comment.