MULTI-POINT BOUNDARY VALUE PROBLEMS OF FRACTIONAL ORDER

TitleMULTI-POINT BOUNDARY VALUE PROBLEMS OF FRACTIONAL ORDER
Publication TypeJournal Article
Year of Publication2008
AuthorsALLISON, JOHN, KOSMATOV, NICKOLAI
Volume12
Issue4
Start Page451
Pagination8
Date Published2008
ISSN1083-2564
AMS34A12, 34A34, 34B10, 45D05
Abstract

In this paper we study multi-point boundary value problems of fractional order with the Riemann-Liouville and Caputo fractional derivatives. The existence results are obtained using the Schauder fixed point theorem.

URLhttp://www.acadsol.eu/en/articles/12/4/8.pdf
Refereed DesignationRefereed
Full Text

REFERENCES
[1] M. Benchohra, J. Henderson, S. K. Ntoyuas, and A. Quahab, Existence results for fractional
order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), 1340–1350.
[2] M. Caputo, Linear models of dissipation whose Q is almost frequency independent (Part II),
Geophysical J. of the Royal Astronomical Society, 13 (1967), 529–539.
[3] D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation,
J. Math. Anal. Appl., 204 (1996), 609–625.
[4] K. Diethelm, A. D. Freed, On the solution of nolinear fractional order differential equations used
in the modelling of viscoplasticity, in: F. Keil, W. Mackens, H. Voss (Eds.), Scientific Computing
in Chemical Engineering II- Computational Fluid Dynamics and Molecular Properties, SpringerVerlag,
Heidelberg, 1999, pp. 217–224.
[5] A. M. A. El-Sayed, M. Gaber, On the finite Caputo and finite Rietz derivatives, Electronic J.
Theoretical Physics, 13 (2006), 81–95.
[6] O. K. Jaradat, A. Al-Omari, S. Momani, Existence of the mild solution for fractional semilinear
initial value problems, Nonlinear Anal., 69 (2008), 3153–3159.
[7] A. A. Kilbas, S. A. Marzan, Nonlinear differential equations with the Caputo fractional derivative
in the space of continuously differentiable functions, Differ. Uravn., 41 (2005), 82–86, (in
Russian); translation in Differ. Equ., 41 (2005), 84–89.
[8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, “Theory and Applications of Fractional Differential
Equations”, North Holland Mathematics Studies, 204, Elsevier, 2006.
[9] A. A. Kilbas, J. J. Trujillo, Differential equations of fractional order: methods, results and
problems, Appl. Anal., 78 (2001), 153–192.
[10] V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal., 69
(2008), 3337–3343.
[11] V. Lakshmikantham, A. S. Vatsala, Basic theory of fractional differential equations, Nonlinear
Anal., 69 (2008), 2677–2682.
[12] K. S. Miller, B. Ross, “An introduction to fractional calculus and fractional differential equations”,
John Wiley & Sons, New York, 1993.
[13] M. D. Ortigueira, J. A. Tenreiro-Machado, J. S´a da Costa, Considerations about the choice of a
differintegrator, Proceedings of the 2nd International Conference on Computational Cybernetics,
Vienna University of Technology, 2004.
[14] I. Podlubny, “Fractional Differential Equations, Mathematics in Sciences and Applications”,
Academic Press, New York, 1999.
[15] J. Sabatier, O. P. Agrawal, J. A. Tenreiro-Machado, “Advances in Fractional Calculus: Theoretical
Developments and Applications in Physics and Engineering”, Springer, The Netherlands, 2007.
[16] S. G. Samko, A. A. Kilbas, O. I. Mirichev, “Fractional Integral and Derivatives (Theory and
Applications)”, Gordon and Breach, Switzerland, 1993.