Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 10, 2009, Pages 4676-4688

  Xu, Xiaojie ^a,b   Jiang, Daqing ^a   Yuan, Chengjun ^c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b CHINA UNIVERSITY OF PETROLEUM   (China)

^c HARBIN UNIVERSITY   (China)

Author keywords

Boundary value problem; Fixed point theorem; Fractional differential equation; Fractional Green's function; Positive solution

Indexed keywords

FIXED POINT THEOREMS; FIXED-POINT THEOREM; FRACTIONAL DIFFERENTIAL EQUATION; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL GREEN'S FUNCTION; LERAY-SCHAUDER NONLINEAR ALTERNATIVE; MULTIPLE POSITIVE SOLUTIONS; POSITIVE SOLUTION; REAL NUMBER; SINGULAR PROBLEM; UNIQUENESS OF SOLUTION;

BOUNDARY VALUE PROBLEMS; NONLINEAR EQUATIONS; NUMBER THEORY; ORDINARY DIFFERENTIAL EQUATIONS;

GREEN'S FUNCTION;

EID: 67651094005     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.03.030     Document Type: Article

References (22)

1. Anatoly Kilbas A., Hari Srivastava M., and Juan Trujillo J. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics studies vol. 204 (2006), Elsevier Science B.V., Amsterdam
2. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic Press, New York and London
3. In: Ross B. (Ed). The Fractional Calculus and its Applications. Lecture Notes in Mathematics vol. 475 (1975), Springer-Verlag, Berlin
4. Nonnenmacher T.F., and Metzler R. On the Riemann-Liouville fractional calculus and some recent applications. Fractals 3 (1995) 557-566
5. Tatom F.B. The relationship between fractional calculus and fractals. Fractals 3 (1995) 217-229
6. Podlubny I. Fractional Differential Equations. Mathematics in Science and Engineering vol. 198 (1999), Academic Press, New york/London/Toronto
7. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integral and Derivatives (Theory and Applications) (1993), Gordon and Breach, Switzerland
8. Agrawal R.P. Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272 (2002) 368-379
9. Babakhani A., and Gejji V.D. Existence of positive solutions of nonlinear fractional differential equations. J. Math. Anal. Appl. 278 (2003) 434-442
10. Delbosco D., and Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204 (1996) 609-625
11. Gejji V.D., and Babakhani A. Analysis of a system of fractional differential equations. J. Math. Anal. Appl. 293 (2004) 511-522
12. Zhang S. The existence of a positive solution for a nonlinear fractional differential equation. J. Math. Anal. Appl. 252 (2000) 804-812
13. Zhang S. Existence of positive solution for some class of nonlinear fractional differential equations. J. Math. Anal. Appl. 278 (2003) 136-148
14. Nakhushev A.M. The Sturm-Liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms. Dokl. Akad. Nauk SSSR 234 (1977) 308-311
15. Bai Z., and Lü H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311 (2005) 495-505
16. Kilbas A.A., and Trujillo J.J. Differential equations of fractional order: Methods, results and problems II. Appl. Anal. 81 (2002) 435-493
17. Agarwal R.P., Benchohra M., and Slimani B.A. Existence results for differential equations with fractional order and impulses. Mem. Differential Equations Math. Phys. 44 (2008) 1-21
18. Benchohra M., Graef J.R., and Hamani S. Existence results for boundary value problems with nonlinear fractional differential equations. Appl. Anal. 87 7 (2008) 851-863
19. Lakshmikantham V., Leela S., and Vasundhara J. Theory of Fractional Dynamic Systems (2009), Cambridge Academic Publishers, Cambridge
20. Krasnosel'skii M.A. Positive Solutions of Operator Equations (1964), Noordhoff, Groningen, Netherlands
21. Cao Z., Jiang D., Yuan C., and O' Regan D. Existence and uniqueness of solutions for singular integral equation. Positivity 12 (2008) 725-732
22. J. Chu, D. O'Regan, Singular integral equations of Hammerstein type and applications to nonlinear conjugate problems, Taiwanese J. Math. (in press)