New uniqueness results of solutions for fractional differential equations with infinite delay

Computers and Mathematics with Applications

Volumn 60, Issue 8, 2010, Pages 2253-2259

  Deng, Jiqin ^a   Qu, Hailiang ^a  

^a XIANGTAN UNIVERSITY   (China)

Author keywords

Existence and uniqueness; Fixed point theorem; Fractional integral; RiemmanLiouville fractional derivatives

Indexed keywords

EXISTENCE AND UNIQUENESS; EXISTENCE AND UNIQUENESS OF SOLUTION; EXISTENCE AND UNIQUENESS RESULTS; FIXED POINT THEOREMS; FIXED POINT THEORY; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL INTEGRALS; INFINITE DELAY; NEUTRAL DIFFERENTIAL EQUATION;

DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS;

NONLINEAR EQUATIONS;

EID: 77957359943     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.08.015     Document Type: Article

References (21)

1. D. Delboso, and L. Rodino Existence and uniqueness for a nonlinear fractional differential equation J. Math. Anal. Appl. 204 1996 609 625
2. K. Diethelm, and N.J. Ford Analysis of fractional differential equations J. Math. Anal. Appl. 265 2002 229 248
3. L. Gaul, P. Klein, and S. Kempfle Damping description involving fractional operators Mech. Syst. Signal Process. 5 1991 81 88
4. W.G. Glockle, and T.F. Nonnenmacher A fractional calculus approach of self-similar protein dynamics Biophys. J. 68 1995 46 53
5. V. Lakshmikantham, and S. Leela A KrasnoselskiiKrein-type uniqueness result for fractional differential equations Nonlinear Anal. 71 2009 3421 3424
6. Mohammed Belmekki, Juan J. Nieto, and Rosana Rodrguez-Lpez Existence of periodic solution for a nonlinear fractional differential equation Bound. Value Probl. 2009 2009 Art. ID 324561
7. A. Arara, M. Benchohra, N. Hamidi, and J.J. Nieto Fractional order differential equations on an unbounded domain Nonlinear Anal. 72 2010 580 586
8. F. Mainardi Fractional calculus: some basic problems in continuum and statistical mechanics A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer-Verlag Wien 291 348
9. F. Metzler, W. Schick, H.G. Kilian, and T.F. Nonnenmacher Relaxation in filled polymers: a fractional calculus approach J. Chem. Phys. 103 1995 7180 7186
10. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Differential Equations 1993 John Wiley New York
11. S.M. Momani, S.B. Hadid, and Z.M. Alawenh Some analytical properties of solutions of differential equations of noninteger order Int. J. Math. Math. Sci. 2004 2004 697 701
12. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
13. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives. Theory and Applications 1993 Gordon and Breach Yverdon
14. K. Schumacher Existence and continuous dependence for differential equations with unbounded delay Arch. Ration. Mech. Anal. 64 1978 315 335
15. J.S. Shin An existence theorem of functional differential equations with infinite delay in a Banach space Funkcial. Ekvac. 30 1987 19 29
16. M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 2008 1340 1350
17. Khalil Ezzinbi, Hamidou Toure, and Issa Zabsonre Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces Nonlinear Anal. 70 2009 2761 2771
18. T.A. Maraaba, F. Jarad, and D. Baleanu On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives Sci. China Ser. A 51 10 2008 1775 1786
19. T. Maraaba, D. Baleanu, and F. Jarad Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives J. Math. Phys. 49 8 2008 Article Number: 083507
20. D. Baleanu, T. Maaraba, and F. Jarad Fractional variational principles with delay J. Phys. A 41 31 2008 Article Number: 315403
21. Jiqin Deng, and Lifeng Ma Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations Appl. Math. Lett. 23 2010 676 680