Eigenvalue of fractional differential equations with p -Laplacian operator

Discrete Dynamics in Nature and Society

Volumn 2013, Issue , 2013, Pages

  Wu, Wenquan ^a   Zhou, Xiangbing ^a  

^a Aba Teachers College   (China)

Author keywords

[No Author keywords available]

Indexed keywords

RHODOCOCCUS RHODOCHROUS;

EID: 84876582149     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2013/137890     Document Type: Article

References (23)

1. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier North-Holland Mathematics Studies MR2218073 10.1016/S0304-0208(06) 80001-0 ZBL1206.26007
2. Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 New York, NY, USA Wiley MR1219954 ZBL0943.82582
3. Podlubny I., Fractional Differential Equations 1999 198 New York, NY, USA Academic Press Mathematics in Science and Engineering MR1658022 ZBL1056.93542
4. Babakhani A., Daftardar-Gejji V., Existence of positive solutions of nonlinear fractional differential equations. Journal of Mathematical Analysis and Applications 2003 278 2 434 442 10.1016/S0022-247X(02)00716-3 MR1974017 ZBL1027.34003 (Pubitemid 36530147)
5. Delbosco D., Rodino L., Existence and uniqueness for a nonlinear fractional differential equation. Journal of Mathematical Analysis and Applications 1996 204 2 609 625 10.1006/jmaa.1996.0456 MR1421467 ZBL0881.34005 (Pubitemid 126163548)
6. El-Sayed A. M. A., Nonlinear functional-differential equations of arbitrary orders. Nonlinear Analysis: Theory, Methods and Applications A 1998 33 2 181 186 10.1016/S0362-546X(97)00525-7 MR1621105 ZBL0934.34055 (Pubitemid 128403304)
7. Lakshmikantham V., Theory of fractional functional differential equations. Nonlinear Analysis: Theory, Methods and Applications A 2008 69 10 3337 3343 10.1016/j.na.2007.09.025 MR2450543 ZBL1162.34344
8. Zhang S., Existence of positive solution for some class of nonlinear fractional differential equations. Journal of Mathematical Analysis and Applications 2003 278 1 136 148 10.1016/S0022-247X(02)00583-8 MR1963470 ZBL1026.34008 (Pubitemid 36445950)
9. Zhang X., Han Y., Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations. Applied Mathematics Letters 2012 25 3 555 560 10.1016/j.aml.2011.09.058 MR2856032 ZBL1244.34009
10. Zhang X., Liu L., Wu Y., The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives. Applied Mathematics and Computation 2012 218 17 8526 8536 10.1016/j.amc.2012.02.014 MR2921344 ZBL1254.34016
11. Bai Z., Lv H., Positive solutions for boundary value problem of nonlinear fractional differential equation. Journal of Mathematical Analysis and Applications 2005 311 2 495 505 10.1016/j.jmaa.2005.02.052 MR2168413 ZBL1079.34048 (Pubitemid 41350217)
12. Zhang X., Liu L., Wu Y., The uniqueness of positive solution for a singular fractional differential system involving derivatives. Communications in Nonlinear Science and Numerical Simulation 2013 18 1400 1409
13. Kaufmann E. R., Mboumi E., Positive solutions of a boundary value problem for a nonlinear fractional differential equation. Electronic Journal of Qualitative Theory of Differential Equations 2008 3 1 11 MR2369417 ZBL1183.34007
14. Bai C., Triple positive solutions for a boundary value problem of nonlinear fractional differential equation. Electronic Journal of Qualitative Theory of Differential Equations 2008 24 1 10 MR2425095 ZBL1183.34005
15. Li C. F., Luo X. N., Zhou Y., Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Computers and Mathematics with Applications 2010 59 3 1363 1375 10.1016/j.camwa.2009.06.029 MR2579500 ZBL1189.34014
16. Wang J., Xiang H., Liu Z., Positive solutions for three-point boundary value problems of nonlinear fractional differential equations with p -Laplacian. Far East Journal of Applied Mathematics 2009 37 1 33 47 MR2583953
17. Wang J., Xiang H., Upper and lower solutions method for a class of singular fractional boundary value problems with p -Laplacian operator. Abstract and Applied Analysis 2010 2010 12 971824 10.1155/2010/971824 MR2720032
18. Chai G., Positive solutions for boundary value problem of fractional differential equation with p -Laplacian operator. Boundary Value Problems 2012 2012, article 18 10.1186/1687-2770-2012-18 MR2904637
19. Zhang X., Liu L., Wiwatanapataphee B., Wu Y., Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives. Abstract and Applied Analysis 2012 2012 16 512127 10.1155/2012/512127 MR2922960 ZBL1242.34015
20. Zhou Y., Existence and uniqueness of solutions for a system of fractional differential equations. Fractional Calculus and Applied Analysis 2009 12 2 195 204 MR2498366
21. Zhang X., Liu L., Wu Y., Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives. Applied Mathematics and Computation 2012 219 4 1420 1433 10.1016/j.amc.2012.07.046 MR2983853
22. Zhou Y., Existence and uniqueness of fractional functional differential equations with unbounded delay. International Journal of Dynamical Systems and Differential Equations 2008 1 4 239 244 10.1504/IJDSDE.2008.022988 MR2502297 ZBL1175.34081
23. Zhang X., Liu L., Wu Y., Lu Y., The iterative solutions of nonlinear fractional differential equations. Applied Mathematics and Computation 2013 219 9 4680 4691 10.1016/j.amc.2012.10.082 MR3001516