Global uniqueness results for fractional order partial hyperbolic functional differential equations

Advances in Difference Equations

Volumn 2011, Issue , 2011, Pages

  Nieto, Juan J ^c   Abbas, Saïd ^a   Benchohra, Mouffak ^b  

^a UNIVERSITY OF SAIDA   (Algeria)

^b UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^c UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79955024126     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1155/2011/379876     Document Type: Article

References (50)

1. Kilbas A. A., Bonilla V., Trukhillo Kh., Nonlinear differential equations of fractional order in the space of integrable functions Rossiskaya Akademiya Nauk. Doklady Akademii Nauk 2000 374 4 445 449
2. Semenchuk N. P., A class of differential equations of nonintegral order Differentsial'nye Uravneniya 1982 18 10 1831 1833
3. Vityuk A. N., Existence of solutions of partial differential inclusions of fractional orders Izvestiya Vysshikh Uchebnykh Zavedeni. Matematika 1997 8 13 19
4. Diethelm K., Freed A. D., Keil F., Mackens W., Voss H., Werther J., On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties 1999 Heidelberg, Germany Springer 217 224
5. Fort J., Prez-LoSaïda J., Isern N., Fronts from integrodifference equations and persistence effects on the Neolithic transition Physical Review E 2007 76 3 10
6. Gaul L., Klein P., Kemple S., Damping description involving fractional operators Mechanical Systems and Signal Processing 1991 5 2 81 88
7. Glockle W. G., Nonnenmacher T. F., A fractional calculus approach to self-similar protein dynamics Biophysical Journal 1995 68 1 46 53
8. Hilfer R., Applications of Fractional Calculus in Physics 2000 River Edge, NJ, USA World Scientific viii+463
9. Mainardi F., Carpinteri A., Mainardi F., Fractional calculus: some basic problems in continuum and statistical mechanics Fractals and fractional calculus in continuum mechanics 1997 378 Vienna, Austria Springer 291 348 CISM Courses and Lectures
10. Metzler R., Schick W., Kilian H. -G., Nonnenmacher T. F., Relaxation in filled polymers: a fractional calculus approach The Journal of Chemical Physics 1995 103 16 7180 7186
11. Vlad M. O., Ross J., Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition Physical Review E 2002 66 6 11
12. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier xvi+523 North-Holland Mathematics Studies
13. Lakshmikantham V., Leela S., Vasundhara J., Theory of Fractional Dynamic Systems 2009 Cambridge, UK Cambridge Academic Publishers
14. Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 New York, NY, USA John Wiley Sons xvi+366 A Wiley-Interscience Publication
15. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives 1993 Yverdon, Switzerland Gordon and Breach Science xxxvi+976
16. Abbas S., Benchohra M., Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative Communications in Mathematical Analysis 2009 7 2 62 72
17. Abbas S., Benchohra M., Darboux problem for perturbed partial differential equations of fractional order with finite delay Nonlinear Analysis: Hybrid Systems 2009 3 4 597 604
18. Abbas S., Benchohra M., Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order Nonlinear Analysis: Hybrid Systems 2010 4 3 406 413
19. Agarwal R. P., Benchohra M., Hamani S., A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions Acta Applicandae Mathematicae 2010 109 3 973 1033
20. Agarwal R. P., Lakshmikantham V., Nieto J. J., On the concept of solution for fractional differential equations with uncertainty Nonlinear Analysis: Theory, Methods Applications 2010 72 6 2859 2862
21. Ahmad B., Nieto J. J., Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions Boundary Value Problems 2009 2009 11
22. Ahmad B., Nieto J. J., Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations Abstract and Applied Analysis 2009 2009 9
23. Ahmad B., Nieto J. J., Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions Computers Mathematics with Applications 2009 58 9 1838 1843
24. Belarbi A., Benchohra M., Ouahab A., Uniqueness results for fractional functional differential equations with infinite delay in Frchet spaces Applicable Analysis 2006 85 12 1459 1470
25. Benchohra M., Graef J. R., Hamani S., Existence results for boundary value problems with non-linear fractional differential equations Applicable Analysis 2008 87 7 851 863
26. Benchohra M., Hamani S., Ntouyas S. K., Boundary value problems for differential equations with fractional order Surveys in Mathematics and Its Applications 2008 3 1 12
27. Benchohra M., Henderson J., Ntouyas S. K., Ouahab A., Existence results for fractional order functional differential equations with infinite delay Journal of Mathematical Analysis and Applications 2008 338 2 1340 1350
28. Chang Y.-K., Nieto J. J., Some new existence results for fractional differential inclusions with boundary conditions Mathematical and Computer Modelling 2009 49 3-4 605 609
29. Diethelm K., Ford N. J., Analysis of fractional differential equations Journal of Mathematical Analysis and Applications 2002 265 2 229 248
30. Heinsalu E., Patriarca M., Goychuk I., Hnggi P., Fractional Fokker-Planck subdiffusion in alternating force fields Physical Review E 2009 79 4
31. Jumarie G., An approach via fractional analysis to non-linearity induced by coarse-graining in space Nonlinear Analysis: Real World Applications 2010 11 1 535 546
32. Kilbas A. A., Marzan S. A., Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions Differentsialnye Uravneniya 2005 41 1 82 86
33. Luchko Y. F., Rivero M., Trujillo J. J., Velasco M. P., Fractional models, non-locality, and complex systems Computers Mathematics with Applications 2010 59 3 1048 1056
34. Magdziarz M., Weron A., Weron K., Fractional Fokker-Planck dynamics: Stochastic representation and computer simulation Physical Review E 2007 75 1
35. Rossikhin Y. A., Shitikova M. V., Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results Applied Mechanics Reviews 2010 63 1 52
36. Vityuk A. N., Golushkov A. V., Existence of solutions of systems of partial differential equations of fractional order Nonlinear Oscillations 2004 7 3 328 335
37. Yu C., Gao G., Existence of fractional differential equations Journal of Mathematical Analysis and Applications 2005 310 1 26 29 (Pubitemid 41149444)
38. Zhang S., Positive solutions for boundary-value problems of nonlinear fractional differential equations Electronic Journal of Differential Equations 2006 36 1 12 (Pubitemid 43448954)
39. Kamont Z., Hyperbolic Functional Differential Inequalities and Applications 1999 486 Dordrecht, The Netherlands Kluwer Academic Publishers xiv+304 Mathematics and Its Applications
40. Czapiski T., On the Darboux problem for partial differential-functional equations with infinite delay at derivatives Nonlinear Analysis: Theory, Methods Applications 2001 44 3 389 398
41. Dawidowski M., Kubiaczyk I., An existence theorem for the generalized hyperbolic equation zxyF(x,y,z) in Banach space Roczniki Polskiego Towarzystwa Matematycznego. Seria I 1990 30 1 41 49
42. Kamont Z., Kropielnicka K., Differential difference inequalities related to hyperbolic functional differential systems and applications Mathematical Inequalities Applications 2005 8 4 655 674 (Pubitemid 41639388)
43. Lakshmikantham V., Pandit S. G., The method of upper, lower solutions and hyperbolic partial differential equations Journal of Mathematical Analysis and Applications 1985 105 2 466 477 (Pubitemid 15598644)
44. Pandit S. G., Monotone methods for systems of nonlinear hyperbolic problems in two independent variables Nonlinear Analysis: Theory, Methods Applications 1997 30 5 2735 2742 (Pubitemid 127406939)
45. Frigon M., Granas A., Rsultats de type Leray-Schauder pour des contractions sur des espaces de Frchet Annales des Sciences Mathmatiques du Qubec 1998 22 2 161 168
46. Henry D., Geometric theory of Semilinear Parabolic Partial Differential Equations 1989 Berlin, Germany Springer
47. Hale J. K., Kato J., Phase space for retarded equations with infinite delay Funkcialaj Ekvacioj 1978 21 1 11 41
48. Hale J. K., Verduyn Lunel S. M., Introduction to Functional-Differential Equations 1993 99 New York, NY, USA Springer x+447 Applied Mathematical Sciences
49. Hino Y., Murakami S., Naito T., Functional-Differential Equations with Infinite Delay 1991 1473 Berlin, Germany Springer x+317 Lecture Notes in Mathematics
50. Lakshmikantham V., Wen L. Z., Zhang B. G., Theory of Differential Equations with Unbounded Delay 1994 298 Dordrecht, The Netherlands Kluwer Academic Publishers xii+385 Mathematics and Its Applications