Existence of solutions of nonlinear fractional differential equations at resonance

Electronic Journal of Qualitative Theory of Differential Equations

Volumn , Issue , 2011, Pages 1-12

  Rui, Wenjuan ^a  

^a CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

Boundary value problems; Coincidence degree theory; Fractional differential equations; Resonance

Indexed keywords

EID: 80053055657     PISSN: None     EISSN: 14173875     Source Type: Journal    
DOI: 10.14232/ejqtde.2011.1.66     Document Type: Article

References (19)

1. R. Metzler, J. Klafter, Boundary value problems for fractional diffusion equations, Phys. A 278, 107-125 (2000).
2. H. Scher, E. Montroll, Anomalous transit-time dispersion in amorphous solids, Phys. Rev. B 12, 2455-2477 (1975).
3. F. Mainardi, Fractional diffusive waves in viscoelastic solids, in: J.L. Wegner, F.R. Norwood (Eds.), Nonlinear Waves in Solids, Fairfield, 93-97 (1995).
4. K. Diethelm, A.D. Freed, On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, in: F. Keil, W. Mackens, H. Voss, J. Werther (Eds.), Scientific Computing in Chemical Engineering IIComputational Fluid Dynamics, Reaction Engineering and Molecular Properties, pp. 217-224. Springer-Verlag, Heidelberg (1999).
5. L. Gaul, P. Klein, S. Kempfle, Damping description involving fractional operators, Mech. Syst. Signal Process. 5, 81-88 (1991).
6. W.G. Glockle, T.F. Nonnenmacher, A fractional calculus approach of self-similar protein dynamics, Biophys. J. 68, 46-53 (1995).
7. F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, pp. 291-348. Springer-Verlag, Wien (1997).
8. F. Metzler, W. Schick, H.G. Kilian, T.F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach, J. Chem. Phys. 103, 7180-7186 (1995).
9. K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, London (1974).
10. R.P. Agarwal, D. O'Regan, S. Stanek, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. Math. Anal. Appl. 371, 57-68 (2010).
11. Z. Bai, H. Lü, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311, 495-505 (2005).
12. E.R. Kaufmann, E. Mboumi, Positive solutions of a boundary value problem for a nonlinear fractional differential equation, Electron. J. Qual. Theory Differ. Equ. 3, 1-11 (2008).
13. H. Jafari, V.D. Gejji, Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method, Appl. Math. Comput. 180, 700-706 (2006).
14. M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Anal. 71, 2391-2396 (2009).
15. S. Liang, J. Zhang, Positive solutions for boundary value problems of nonlinear fractional differential equation, Nonlinear Anal. 71, 5545-5550 (2009).
16. S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differ. Equ. 36, 1-12 (2006).
17. N. Kosmatov, A boundary value problem of fractional order at resonance, Electron. J. Differ. Equ. 135, 1-10 (2010).
18. J. Mawhin, Topological degree and boundary value problems for nonlinear differential equations in topological methods for ordinary differential equations, Lecture Notes in Math. 1537, 74-142 (1993).
19. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands (2006).