Uniqueness of positive solutions for fractional q-difference boundary-value problems with p-laplacian operator

Electronic Journal of Differential Equations

Volumn 2013, Issue , 2013, Pages

  Miao, Fenghua ^a   Liang, Sihua ^a  

^a CHANGCHUN NORMAL UNIVERSITY   (China)

Author keywords

Fractional q difference equations; Partially ordered sets;

Indexed keywords

EID: 84880942046     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. R. P. Agarwal; Certain fractional q-integrals and q-derivatives, Proc. Cambridge Philos. Soc., 66 (1969) 365-370.
2. R. P. Agarwal, D. O'Regan, P. J. Y. Wong; Positive Solutions of Differential, Difference and Integral Equations, Kluwer Acad. Publ., Dordrecht, 1999.
3. W. A. Al-Salam; Some fractional q-integrals and q-derivatives, Proc. Edinburgh Math. Soc., (2) 15 (1966/1967) 135-140.
4. F. M. Atici, P. W. Eloe; Fractional q-calculus on a time scale, J. Nonlinear Math. Phys., 14 (3) (2007) 333-344.
5. M. Benchohra, J. Henderson, S. K. Ntouyas, A. Ouahab; Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008) 1340-1350.
6. J. Caballero Mena, J. Harjani, K. Sadarangani; Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems, Boundary Value Problems, Vol. 2009 (2009), Article ID 421310, 10 pages, doi:10.1155/2009/421310.
7. A. M. A. El-Sayed, A. E. M. El-Mesiry, H. A. A. El-Saka; On the fractional-order logistic equation, Appl. Math. Letters, 20 (2007) 817-823.
8. M. El-Shahed; Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstract and Applied Analysis, Vol. 2007, Article ID 10368, 8 pages, 2007, doi: 10.1155/2007/10368
9. T. Ernst; The History of q-Calculus and a New Method, U. U. D. M. Report 2000:16, ISSN 1101-3591, Department of Mathematics, Uppsala University, 2000.
10. R. A. C. Ferreira; Nontrivial solutions for fractional q-difference boundary-value problemsElectron, J. Qual. Theory Differ. Equ., (70) (2010) 10 pp.
11. R. A. C. Ferreira; Positive solutions for a class of boundary value problems with fractional q-differences, Computers and Mathematics with Applications. preprint.
12. J. Harjani, K. Sadarangani; Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal., 71 (2009) 3403-3410.
13. F.H. Jackson; On q-functions and a certain difference operator. Trans. Roy Soc. Edin., 46 (1908) 253-281.
14. F. H. Jackson; On q-definite integrals, Quart. J. Pure and Appl. Math., 41 (1910) 193-203.
15. V. Kac, P. Cheung; Quantum Calculus, Springer, New York, 2002.
16. 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.
17. V. Lakshmikantham, A. S. Vatsala; Basic theory of fractional differential equations, Nonlinear Anal., 69 (2008) 2677-2682.
18. V. Lakshmikantham, A. S. Vatsala; General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Letters, 21 (2008) 828-834.
19. V. Lakshmikantham; Theory of fractional functional differential equations, Nonlinear Anal., 69 (2008) 3337-3343.
20. S. Liang, J. H. Zhang; Positive solutions for boundary value problems of nonlinear fractional differential equation, Nonlinear Anal., 71 (2009) 5545-5550.
21. C. F. Li, X. N. Luo, Y. Zhou; Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Comput. Math. Appl., 59 (2010) 1363-1375.
22. J. J. Nieto, R. Rodríguez-López; Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005) 223-239.
23. J. J. Nieto, R. Rodríguez-López; Fixed point theorems in ordered abstract spaces, Proceedings of the American Mathematical Society, vol. 135, no. 8 (2007) 2505-2517.
24. D. O'Regan, A. Petrusel; Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008) 1241-1252.
25. I. Podlubny; Fractional Differential Equations, Mathematics in Sciences and Engineering, 198, Academic Press, San Diego,1999.
26. P. M. Rajković, S. D. Marinković, M. S. Stanković; Fractional integrals and derivatives in q-calculus, Appl. Anal. Discrete Math., 1 (1) (2007) 311-323.
27. S. G. Samko, A. A. Kilbas, O. I. Marichev; Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
28. S. Zhang; Existence of solution for a boundary value problem of fractional order, Acta Mathematica Scientia, 26 (2006) 220-228.
29. Y. Zhou; Existence and uniqueness of fractional functional differential equations with unbounded delay, Int. J. Dyn. Syst. Differ. Equ., 1 (2008) 239-244.