NONLOCAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ARBITRARY FRACTIONAL ORDER
Abstract
In this paper, we investigate the existence and uniqueness of some nonlocal boundary condition for fractional integro-di erential equations with any order. The results are obtained by using xed point theorems. An example is introduced to illustrate the theorem.
Keywords
References
- [1] Agrawal, R. P., Benchohra, M., Hamani, S., Boundary value problems for fractional dieren- tial equations, Georgian Mathematical Journal, 16(3)(2009), 401-411.
- [2] Agarwal, R. P., Ahmad B., Existence theory for anti-periodic boundary value problems of fractional dierential equations and inclusions, Computers & Mathematics with Applica- tions, 62(2011), 1200-1214.
- [3] Balachandran, K., Park, J. Y., Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Analysis, 71(2009), 4471-4475.
- [4] Benchohra, M., Hamani, S., and Ntouyas S. K., Boundary value problems for dierential equations with fractional order and nonlocal conditions, Nonlinear Analysis, 71(2009), 2391- 2396.
- [5] N'guerekata, G. M., A Cauchy problem for some fractional abstract dierential equation with nonlocal condition, Nonlinear Analysis, 70(2009), 1873-1876.
- [6] Delbosco, D., Rodino, L., Existence and uniqueness for a fractional dierential equation, Journal of Mathematical Analysis and Applications, 204(1996), 609-625.
- [7] Matar M. M., Trujillo, J. J.,Existence of local solutions for dierential equations with arbi- trary fractional order, Arabian Journal of Mathematics, DOI 10.1007/s40065-015-0139-4
- [8] Jaradat, O. K., Al-Omari, A., and Momani, S., Existence of the mild solution for fractional semilinear initial value problem, Nonlinear Analysis, 69(2008), 3153-3159.
Details
Primary Language
English
Subjects
Engineering
Journal Section
Research Article
Authors
Mohammed M. Matar
*
This is me
Palestine
Publication Date
April 1, 2016
Submission Date
July 10, 2014
Acceptance Date
-
Published in Issue
Year 2016 Volume: 4 Number: 1
