EXISTENCE AND UNIQUENESS RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH SEPARATED BOUNDARY CONDITIONS

TitleEXISTENCE AND UNIQUENESS RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH SEPARATED BOUNDARY CONDITIONS
Publication TypeJournal Article
Year of Publication2009
AuthorsAHMAD, BASHIR, SIVASUNDARAM, S
Secondary TitleCommunications in Applied Analysis
Volume13
Issue1
Start Page121
Pagination128
Date Published01/2009
Type of Workscientific: mathematics
ISSN1083–2564
AMS34A34, 34B15
Abstract
This paper studies existence and uniqueness results in a Banach space for a two-point boundary value problem involving a nonlinear fractional differential equation given by
Our results are based on contraction mapping principle and Krasnoselskii’s fixed point theorem.
URLhttp://www.acadsol.eu/en/articles/13/1/12.pdf
Short TitleRESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS
Refereed DesignationRefereed
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REFERENCES

[1] Z. Bai, H. Lu, Positive solutions for boundary value problems of nonlinear fractional differential equations, J. Math. Anal. Appl. 311 (2005) 495–505.
[2] V. Gafiychuk, B. Datsko, V. Meleshko, Mathematical modeling of time fractional reaction-diffusion systems, J. Comput. Appl. Math. (in press).
[3] V. D. Gejji, Positive solutions of a system of non-autonomous fractional differential equations, J. Math. Anal. Appl. 302 (2005) 56–64.
[4] R. W. Ibrahim, M. Darus, Subordination and superordination for univalent solutions for fractional differential equations. J. Math. Anal. Appl. (in press).
[5] A. A. Kilbas, H. M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
[6] S. Ladaci, J. L. Loiseau, A. Charef, Fractional order adaptive high-gain controllers for a class of linear systems, Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 707–714.
[7] M. P. Lazarevic, Finite time stability analysis of PD α fractional control of robotic time -delay systems, Mech. Res. Comm. 33(2006) 269–279.
[8] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
[9] S. Z. Rida, H. M. El-Sherbiny, A. A. M. Arafa, On the solution of the fractional nonlinear Schr ̈odinger equation, Physics Letters A 372 (2008) 553–558.
[10] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
[11] S. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equations, Electronic J. Differential Equations 2006(2006), No. 36, 1–12.