Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis

Nonlinear Analysis, Theory, Methods and Applications

Volumn 74, Issue 17, 2011, Pages 5975-5986

  Kou, Chunhai ^a   Zhou, Huacheng ^a   Yan, Ye ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

Fractional differential equation; Global existence; Half axis; Initial value problem

Indexed keywords

BASIC THEORY; EXISTENCE OF SOLUTIONS; EXISTENCE RESULTS; FIXED POINT THEOREMS; FRACTIONAL DIFFERENTIAL EQUATIONS; GLOBAL EXISTENCE; GLOBAL EXISTENCE OF SOLUTIONS; HALF-AXIS; INITIAL VALUES; RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES; STABILITY ANALYSIS; SUFFICIENT CONDITIONS;

BANACH SPACES; INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 80051578253     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2011.05.074     Document Type: Article

References (38)

1. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific
2. L. Gaul, P. Klein, and S. Kempfle Damping description involving fractional operators Mech. Syst. Signal Process. 5 1991 81 88
3. K. Diethelm, and A.D. Freed On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity F. Keil, W. Mackens, H. Voss, J. Werther, Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties 1999 Springer-Verlag Heidelberg pp. 217307
4. R.C. Koeller Application of fractional calculus to the theory of viscoelasticity J. Appl. Mech 51 1984 299 307
5. P. Kumar, and O.P. Agrawal An approximate method for numerical solution of fractional differential equations Signal Process. 86 2006 2602 2610
6. I. Podlubny Geometric and physical interpretation of fractional integration and fractional differentiation Fract. Calc. Appl. Anal. 5 2002 367 386
7. 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
8. A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematics Studies vol. 204 2006 Elsevier Science B.V Amsterdam
9. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Differential Equations 1993 John Wiley New York
10. I. Podlubny Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications 1999 Academic Press
11. V. Lakshmikantham, S. Leela, and J. Vasundhara Theory of Fractional Dynamic Systems 2009 Cambridge Academic Publishers Cambridge
12. V. Lakshmikantham, and A.S. Vatsala Basic theory of fractional differential equations Nonlinear Anal. 69 2008 2677 2682
13. A.A. Kilbas, and J.J. Trujillo Differential equations of fractional order: Methods, results and problems I Appl. Anal. 78 2001 153 192
14. A.A. Kilbas, and J.J. Trujillo Differential equations of fractional order: Methods, results and problems II Appl. Anal. 81 2002 435 493
15. H.M. Srivastava, and R.K. Saxena Operators of fractional integration and their applications Appl. Math. Comput. 118 2001 1 52
16. R.P. Agarwal, M. Benchohra, and B.A. Slimani Existence results for differential equations with fractional order and impulses, Mem. Differential Equations Math. Phys. 44 2008 1 21
17. A. Ouahab Some results for fractional boundary value problem of differential inclusions Nonlinear Anal. 69 2008 3877 3896
18. A.M.A. El-Sayed On the fractional differential equation Appl. Math. Comput. 49 1992 205 213
19. A.M.A. El-Sayed Fractional order diffusion-wave equations Internat. J. Theoret. Phys. 35 1996 311 322
20. A.M.A. El-Sayed Nonlinear functional differential equations of arbitrary orders Nonlinear Anal. 33 1998 181 186
21. J.J. Nieto Maximum principles for fractional differential equations derived from Mittag-Leffler functions Appl. Math. Lett. 23 2010 1248 1251
22. C. Li, and W. Deng Remarks on fractional derivatives Appl. Math. Comput. 187 2007 777 784
23. N. Kosmatov Integral equations and initial value problems for nonlinear differential equations of fractional order Nonlinear Anal. 70 2009 2521 2529
24. M. Muslim, C. Conca, and A.K. Nandakumaran Approximate of solutions to fractional integral equation Comput. Math. Appl. 59 2010 1236 1244
25. M. Stojanovi Existence-uniqueness result for a nonlinear n-term fractional equation J. Math. Anal. Appl. 353 2009 244 245
26. D. Delbosco, and L. Rodino Existence and uniqueness for a nonlinear fractional differential equation J. Math. Anal. Appl. 204 1996 609 625
27. A. Babakhani, and V.D. Gejji Existence of positive solutions of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 434 442
28. C. Yu, and G. Gao Existence of fractional differential equations J. Math. Anal. Appl. 310 2005 26 29
29. C.H Kou, J. Liu, and Y. Ye Existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations Disc. Dyn. Nat. Soc. 2010 Article ID 142175, 15 pages
30. A.A. Kilbas, B. Bonilla, and J.J. Trujillo Existence and uniqueness theorems for nonlinear fractional differential equations Demonstratio Math. 33 3 2000 538 602
31. S.D. Eidelman, and A.N. Kochubei Cauchy problem for fractional diffusion equations J. Differential Equations 199 2004 211 255
32. S.Q. Zhang Monotone iterative method for initial value problem involving RiemannLouville derivatives Nonlinear Anal. 71 2009 2087 2093
33. Z.L. Wei, Q.D. Li, and J.L. Che Initial value problems for fractional differential equations involving RiemannLiouville sequential fractional derivative J. Math. Anal. Appl. 367 2010 260 272
34. X. Zhao, and W. Ge Unbounded solutions for fractional bounded value problems on the infinite interval Acta Appl. Math. 109 2010 495 505
35. A. Arara, M. Benchohra, N. Hamidi, and J.J. Nieto Fractional order differential equations on an unbounded domain Nonlinear Anal. 72 2010 580 586
36. R.P Agarwal, and D.O Regan Infinite Interval Problems for Differential, Difference and Integral Equations 2001 Kluwer Academic Publishers Dordrecht
37. R.P Agarwal, and D.O Regan Boundary value problems of nonsingular type on the semi-infinite interval Tohoku. Math. J. 51 1999 391C397
38. A. Granas, and J. Dugundji Fixed Point Theory 2003 Springer Verlag