Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives

Journal of Mathematical Physics

Volumn 49, Issue 8, 2008, Pages

  Maraaba, Thabet ^a   Baleanu, Dumitru ^a,b   Jarad, Fahd ^a  

^a CANKAYA UNIVERSITY   (Turkey)

^b INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50849097037     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2970709     Document Type: Article

References (27)

1. S. G. Samko, A. A. Kilbasand, and O. I. Marichev, Fractional Integrals and Derivatives-Theory and Applications (Gordon and Breach, Linghorne, PA, 1993).
2. I. Podlubny, Fractional Differential Equations (Academic, San Diego, CA, 1999).
3. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Mathematics Studies Vol. 204 (North-Holland, Amsterdam, 2006).
4. G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, Oxford, 2005).
5. R. L. Magin, Fractional Calculus in Bioengineering (Begell, Connecticut, 2006).
6. F. Mainardi, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/0960-0779(95)00125-5 7, 1461 (1996).
7. A. A. Kilbas, M. Rivero, and J. J. Trujillo, Fractional Calculus Appl. Anal. ZZZZZZ 1311-0454 6, 363 (2003).
8. M. F. Silva, J. A. T. Machado, and A. M. Lopes, Robotica 23, 595 (2005). 0263-5747
9. O. P. Agrawal and D. Baleanu, J. Vib. Control JVCOFX 1077-5463 10.1177/1077546307077467 13, 1269 (2007).
10. E. Scalas, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/j.chaos. 2007.01.047 34, 33 (2007).
11. K. Diethelm, N. J. Ford, A. D. Freed, and Y. Luchko, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 10.1016/j.cma.2004.06.006 194, 743 (2005).
12. N. Heymans and I. Podlubny, Rheol. Acta RHEAAK 0035-4511 10.1007/s00397-005-0043-5 45, 765 (2006).
13. F. Riewe, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.1890 53, 1890 (1996).
14. M. Klimek, Czech. J. Phys. CZLIA6 0011-4626 10.1023/A:1013378221617 51, 1348 (2001).
15. O. P. Agrawal, J. Math. Anal. Appl. JMANAK 0022-247X 10.1016/S0022- 247X(02)00180-4 272, 368 (2002).
16. D. Baleanu, Signal Process. SPRODR 0165-1684 10.1016/j.sigpro.2006.02.008 86, 2632 (2006).
17. S. I. Muslih and D. Baleanu, Czech. J. Phys. CZLIA6 0011-4626 10.1007/s10582-005-0067-1 55, 633 (2005).
18. D. Baleanu and S. I. Muslih, Phys. Scr. PHSTBO 0031-8949 10.1238/Physica.Regular.072a00119 72, 119 (2005).
19. D. Baleanu, S. I. Muslih, and K. Tas, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2356797 47, 103503 (2006).
20. E. M. Rabei, K. I. Nawafleh, R. S. Hijjawi, S. I. Muslih, and D. Baleanu, J. Math. Anal. Appl. JMANAK 0022-247X 10.1016/j.jmaa.2006.04.076 327, 891 (2007).
21. S. I. Muslih and D. Baleanu, J. Math. Anal. Appl. JMANAK 0022-247X 10.1016/j.jmaa.2004.09.043 304, 599 (2005).
22. T. M. Atanackovic and B. Stankovic, Z. Angew. Math. Mech. 87, 537 (2007). 0044-2267
23. D. Baleanu and J. J. Trujillo, Nonlinear Dyn. NODYES 0924-090X 10.1007/s11071-007-9281-7 52, 331 (2008).
24. R. D. Driver, Ordinary and Delay Differential Equations, Applied Mathematical Sciences Vol. 20 (Springer, Berlin, 1977).
25. W. Deng, C. Li, and J. Lu, Nonlinear Dyn. NODYES 0924-090X 10.1007/s11071-006-9094-0 48, 409 (2007).
26. T. Maraaba (Abdeljawad), 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: Math., Phys., Astron. SCAAFF 1006-9283 (in press).
27. I. Podlubny, personal communication (11 October 2007).