Positive solutions of nonlinear boundary value problems for delayed fractional q-difference systems

Advances in Difference Equations

Volumn 2014, Issue 1, 2014, Pages

  Yuan, Qiaozhen ^a   Yang, Wengui ^a  

^a Sanmenxia Polytechnic   (China)

Author keywords

Boundary value problems; Fixed point theorems; Fractional q difference systems; Positive solutions

Indexed keywords

EID: 84899513951     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2014-51     Document Type: Article

References (34)

1. Agarwal, RP, Ahmad, B: Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl. 62, 1200-1214 (2011)
2. Agarwal, RP, O'Regan, D, Staněk, S: Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations. J. Math. Anal. Appl. 371, 57-68 (2010)
3. Agarwal, RP, Lakshmikantham, V, Nieto, JJ: On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. 72, 2859-2862 (2010)
4. Ahmad, B, Nieto, JJ, Pimentel, J: Some boundary value problems of fractional differential equations and inclusions. Comput. Math. Appl. 62, 1238-1250 (2011)
5. Ahmad, B, Nieto, JJ: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Bound. Value Probl. 2009, Article ID 708576 (2009)
6. Ahmad, B, Ntouyas, S, Assolami, A: Caputo type fractional differential equations with nonlocal Riemann-Liouville integral boundary conditions. J. Appl. Math. Comput. (2013). doi:10.1007/s12190-012-0610-8
7. Ouyang, Z, Chen, Y, Zou, S: Existence of positive solutions to a boundary value problem for a delayed nonlinear fractional differential system. Bound. Value Probl. 2011, Article ID 475126 (2011)
8. Jackson, FH: On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 46, 253-281 (1908)
9. Jackson, FH: On q-definite integrals. Q. J. Pure Appl. Math. 41, 193-203 (1910)
10. Kac, V, Cheung, P, Quantum Calculus. Springer, New York (2002)
11. Al-Salam, WA: Some fractional q-integrals and q-derivatives. Proc. Edinb. Math. Soc. 15(2), 135-140 (1966/1967)
12. Agarwal, RP: Certain fractional q-integrals and q-derivatives. Proc. Camb. Philos. Soc. 66, 365-370 (1969)
13. Abdeljawad, T, Benli, B, Baleanu, D: A generalized q-Mittag-Leffler function by q-Caputo fractional linear equations. Abstr. Appl. Anal. 2012, Article ID 546062 (2012)
14. Rajković, PM, Marinković, SD, Stanković, MS: On q-analogues of Caputo derivative and Mittag-Leffler function. Fract. Calc. Appl. Anal. 10, 359-373 (2007)
15. Rajković, PM, Marinković, SD, Stanković, MS: Fractional integrals and derivatives in q-calculus. Appl. Anal. Discrete Math. 1, 311-323 (2007)
16. Atici, FM, Eloe, PW: Fractional q-calculus on a time scale. J. Nonlinear Math. Phys. 14, 333-344 (2007)
17. El-Shahed, M, Al-Askar, FM: On the existence and uniqueness of solutions for q-fractional boundary value problem. Int. J. Math. Anal. 5, 1619-1630 (2011)
18. Zhao, Y, Chen, H, Zhang, Q: Existence results for fractional q-difference equations with nonlocal q-integral boundary conditions. Adv. Differ. Equ. 2013, Article ID 48 (2013)
19. Zhao, Y, Chen, H, Zhang, Q: Existence and multiplicity of positive solutions for nonhomogeneous boundary value problems with fractional q-derivative. Bound. Value Probl. 2013, Article ID 103 (2013)
20. Yang, W: Positive solutions for boundary value problems involving nonlinear fractional q-difference equations. Differ. Equ. Appl. 5, 205-219 (2013)
21. Yang, W: Positive solution for fractional q-difference boundary value problems with φ-Laplacian operator. Bull. Malays. Math. Soc. 36(4), 1195-1203 (2013)
22. El-Shahed, M, Al-Askar, FM: Positive solutions for boundary value problem of nonlinear fractional q-difference equation. ISRN Math. Anal. 2011, Article ID 385459 (2011)
23. Graef, JR, Kong, L: Positive solutions for a class of higher order boundary value problems with fractional q-derivatives. Appl. Math. Comput. 218, 9682-9689 (2012)
24. Ma, J, Yang, J: Existence of solutions for multi-point boundary value problem of fractional q-difference equation. Electron. J. Qual. Theory Differ. Equ. 92, 1-10 (2011)
25. Zhao, Y, Ye, G, Chen, H: Multiple positive solutions of a singular semipositone integral boundary value problem for fractional q-derivatives equation. Abstr. Appl. Anal. 2013, Article ID 643571 (2013)
26. Ferreira, RAC: Nontrivial solutions for fractional q-difference boundary value problems. Electron. J. Qual. Theory Differ. Equ. 70, 1-10 (2010)
27. Ferreira, RAC: Positive solutions for a class of boundary value problems with fractional q-differences. Comput. Math. Appl. 61, 367-373 (2011)
28. Liang, S, Zhang, J: Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences. J. Appl. Math. Comput. 40, 277-288 (2012)
29. Ahmad, B, Ntouyas, S, Purnaras, I: Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations. Adv. Differ. Equ. 2012, Article ID 140 (2012)
30. Alsaedi, A, Ahmad, B, Al-Hutami, H: A study of nonlinear fractional q-difference equations with nonlocal integral boundary conditions. Abstr. Appl. Anal. 2013, Article ID 410505 (2013)
31. Agarwal, RP, Meehan, M, O'Regan, D: Fixed Point Theory and Applications. Cambridge Tracts in Mathematics, vol. 141. Cambridge University Press, Cambridge (2001)
32. Li, C, Luo, X, Zhou, Y: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Comput. Math. Appl. 59, 1363-1375 (2010)
33. Granas, A, Guenther, RB, Lee, JW: Some general existence principles in the Caratheodory theory of nonlinear differential systems. J. Math. Pures Appl. 70, 153-196 (1991)
34. Krasnosel'skii, MA: Topological Methods in the Theory of Nonlinear Integral Equations. Macmillan Co., New York (1964)