Multiple solutions for fractional differential equations with nonlinear boundary conditions

Computers and Mathematics with Applications

Volumn 59, Issue 8, 2010, Pages 2880-2886

  Liu, Xiping ^a   Jia, Mei ^a  

^a UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

Author keywords

Amann theorem; Caputo derivative; Fractional differential equations; Method of upper and lower solutions; Multiple solutions; Nonlinear boundary conditions

Indexed keywords

CAPUTO DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; METHOD OF UPPER AND LOWER SOLUTIONS; MULTIPLE SOLUTIONS; NON-LINEAR BOUNDARY CONDITIONS;

NONLINEAR EQUATIONS;

BOUNDARY CONDITIONS;

EID: 77950189007     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.02.005     Document Type: Article

References (11)

1. El-Sayed A.M.A. Nonlinear functional differential equations of arbitrary orders. Nonlinear Anal. 33 (1998) 181-186
2. Kilbas A.A., and Trujillo J.J. Differential equations of fractional order: Methods, results and problems I. Appl. Anal. 78 (2001) 153-192
3. Kilbas A.A., and Trujillo J.J. Differential equations of fractional order: Methods, results and problems II. Appl. Anal. 81 (2002) 435-493
4. Podlubny I. Fractional Differential Equations. Mathematics in science and Engineering vol. 198 (1999), Academic Press, New York, London, Toronto
5. Lakshmikantham V., and Vatsalab A.S. Basic theory of fractional differential equations. Nonlinear Anal. 69 (2008) 2677-2682
6. Lakshmikantham V. Theory of fractional functional differential equations. Nonlinear Anal. 69 (2008) 3337-3343
7. Lakshmikantham V., and Vatsalab A.S. General uniqueness and monotone iterative technique for fractional differential equations. Appl. Math. Lett. 21 (2008) 828-834
8. Bai Z., and Lü H. Positive solutions for boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311 (2005) 495-505
9. Xu X., Jiang D., and Yuan C. Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation. Nonlinear Anal. 71 (2009) 4676-4688
10. Amann H. Fixed point equation and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976) 620-709
11. Xu X., and Sun J. Solutions for an operator equation under the conditions of pairs of paralleled lower and upper solutions. Nonlinear Anal. 69 (2008) 2251-2266