The uniqueness of positive solution for a singular fractional differential system involving derivatives

Communications in Nonlinear Science and Numerical Simulation

Volumn 18, Issue 6, 2013, Pages 1400-1409

  Zhang, Xinguang ^a   Liu, Lishan ^b   Wu, Yonghong ^c  

^a YANTAI UNIVERSITY   (China)

^b QUFU NORMAL UNIVERSITY   (China)

^c CURTIN UNIVERSITY   (Australia)

Author keywords

Existence and uniqueness of positive solution; Fractional differential system; Mixed monotone operator

Indexed keywords

DIFFERENTIAL EQUATIONS;

DIFFERENTIAL SYSTEMS; EXISTENCE AND UNIQUENESS; EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION; FIXED POINTS THEOREMS; FRACTIONAL DIFFERENTIAL; FRACTIONAL DIFFERENTIAL SYSTEM; MIXED MONOTONE OPERATOR; UNIQUENESS OF POSITIVE SOLUTION;

FIXED POINT ARITHMETIC;

EID: 84872405408     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.08.033     Document Type: Article

References (15)

1. Podlubny I. Fractional differential equations. Mathematics in science and engineering 1999, Academic Press, New York, London, Toronto.
2. Miller K., Ross B. An introduction to the fractional calculus and fractional differential equations 1993, Wiley, New York.
3. Hartley T.T., Lorenzo C.F., Qammer H.K. Chaos in fractional order Chuaps system. IEEE Trans Circ Syst I: Fund Theory Appl 1995, 42(8):485.
4. Caputo M. Free modes splitting and alterations of electro chemically polarizable media. Rend Fis Acc Lincei 1993, 4:89.
5. Kilbas A., Srivastava H., Trujillo J. Theory and applications of fractional differential equations 2006, Elsevier B.V., Netherlands.
6. Li C., Luo X., Zhou Y. Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Comput Math Appl 2010, 59:1363-1375.
7. Rehman M., Khan R. Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations. Appl Math Lett 2010, 23:1038-1044.
8. Ahmad B., Nieto J. Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput Math Appl 2009, 58:1838-1843.
9. Zhang X., Liu L., Wu Y. Multiple positive solutions of a singular fractional differential equation with negatively perturbed term. Math Comput Model 2012, 55:1263-1274.
10. Goodrich C. Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. Comput Math Appl 2011, 61:191-202.
11. Goodrich C. Positive solutions to boundary value problems with nonlinear boundary conditions. Nonlinear Anal 2012, 75:417-432.
12. Ahmad B., Nieto J. Existence results for higher order fractional differential inclusions with nonlocal boundary conditions. Nonlinear Stud 2010, 17:131-138.
13. Salem, Hussein A. On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies. J Comput Appl Math 2009, 224:565-572.
14. Zhang X., Han Y. Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations. Appl Math Lett 2012, 25:555-560.
15. Jiang W. The existence of solutions to boundary value problems of fractional differential equations at resonance. Nonlinear Anal 2011, 74:1987-1994.