Employing of some basic theory for class of fractional differential equations

Advances in Difference Equations

Volumn 2011, Issue , 2011, Pages

  Babakhani, Azizollah ^a   Baleanu, Dumitru ^b,c  

^a BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

^b CANKAYA UNIVERSITY   (Turkey)

^c INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953281443     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1155/2011/296353     Document Type: Article

References (25)

1. Glockle W. G., Nonnenmacher T. F., A fractional calculus approach to self-similar protein dynamics Biophysical Journal 1995 68 1 46 53
2. Hilfe R., Applications of Fractional Calculus in Physics 2000 River Edge, NJ, USA World Scientific viii+463
3. 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
4. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering
5. Podlubny I., Geometric and physical interpretation of fractional integration and fractional differentiation Fractional Calculus Applied Analysis 2002 5 4 367 386
6. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science B.V. xvi+523 North-Holland Mathematics Studies
7. Lakshmikantham V., Leela S., Vasundhara J., Theory of Fractional Dynamic Systems 2009 Cambridge, UK Cambridge Academic
8. 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
9. Daftardar-Gejji V., Babakhani A., Analysis of a system of fractional differential equations Journal of Mathematical Analysis and Applications 2004 293 2 511 522 (Pubitemid 38613236)
10. Babakhani A., Enteghami E., Existence of positive solutions for multiterm fractional differential equations of finite delay with polynomial coefficients Abstract and Applied Analysis 2009 2009 12
11. Babakhani A., Positive solutions for system of nonlinear fractional differential equations in two dimensions with delay Abstract and Applied Analysis 2010 2010 16
12. Baleanu D., Golmankhaneh A. K., Nigmatullin R., Golmankhaneh A. K., Fractional Newtonian mechanics Central European Journal of Physics 2010 8 1 120 125
13. Baleanu D., Trujillo J. I., A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives Communications in Nonlinear Science and Numerical Simulation 2010 15 5 1111 1115
14. Baleanu D., New applications of fractional variational principles Reports on Mathematical Physics 2008 61 2 199 206
15. 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
16. Bleanu D., Mustafa O. G., On the global existence of solutions to a class of fractional differential equations Computers Mathematics with Applications 2010 59 5 1835 1841
17. 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
18. Ouahab A., Some results for fractional boundary value problem of differential inclusions Nonlinear Analysis: Theory, Methods Applications 2008 69 11 3877 3896
19. 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
20. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives 1993 Yverdon, Switzerland Gordon and Breach Science xxxvi+976
21. 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
22. 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
23. Heymans N., Podlubny I., Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives Rheologica Acta 2006 45 5 765 771 (Pubitemid 44027219)
24. Lakshmikantham V., Vatsala A. S., Basic theory of fractional differential equations Nonlinear Analysis: Theory, Methods Applications 2008 69 8 2677 2682
25. Babakhani A., Daftardar-Gejji V., Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients Electronic Journal of Differential Equations 2006 2006 129 1 12