Monotone Iterative Technique for Riemann-Liouville Fractional Integro-Differential Equations with Advanced Arguments

Results in Mathematics

Volumn 63, Issue 3-4, 2013, Pages 1277-1287

  Liu, Zhenhai ^a   Sun, Jihua ^a   Szántó, Iván ^b  

^a GUANGXI UNIVERSITY FOR NATIONALITIES   (China)

^b DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

Extremal solutions; Monotone iterative technique; Nonlinear boundary value problems; Riemann Liouville fractional derivatives

Indexed keywords

EID: 84878413818     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/s00025-012-0268-4     Document Type: Article

References (26)

1. Ahmad B., Nieto J. J.: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Comput. Math. Appl. 58(9), 1838-1843 (2009).
2. Belmekki, M., Nieto J. J., Rodriguez-Lopez, R.: Existence of periodic solutions for a nonlinear fractional differential equation. Boundary Value Probl. (2009) (Art. ID. 324561).
3. Glockle W. G., Nonnenmacher T. F.: A fractional calculus approach of self-similar protein dynamics. Biophys. J. 68, 46-53 (1995).
4. Hilfer R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000).
5. Jankowski T.: Advanced differential equations with nonlinear boundary conditions. J. Math. Anal. Appl. 304, 490-503 (2005).
6. Jankowski T.: First-order impulsive ordinary differential equations with advanced arguments. J. Math. Anal. Appl. 331, 1-12 (2007).
7. Kilbsa A. A., Srivastava H. M., Trujillo J. J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).
8. Kosmatov N.: Integral equations and initial value problems for nonlinear differential equations of fractional order. Nonlinear Anal. 70(7), 2521-2529 (2009).
9. Lakshmikantham V., Vatsala A. S.: Basic theory of fractional differential equations. Nonlinear Anal. TMA 69(8), 2677-2682 (2008).
10. Ladde G. S., Lakshmikantham V., Vatsala A. S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman pub. Co., Boston (1985).
11. Lakshmikanthan V., Vatsala A. S.: General uniqueness and monotone iterative technique for fractional differential equations. Appl. Math. Lett. 21, 828-834 (2008).
12. Lakshmikanthan V., Leela S., Vasundhara J.: Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009).
13. Liu, Z. H., Sun, J. H.: Nonlinear boundary value problems of fractional functional integro-differential equations. Comput. Math. Appl. doi: 10. 1016/j. camwa. 2012. 02. 026.
14. McRae, F. A.: Monotone iterative technique and existence results for fractional differential equations. Nonlinear Anal. (2009). doi: 10. 1016/j. na. 2009. 05. 074.
15. Podlubny I.: Fractional Differential Equations. Academic Press, San Diego (1999).
16. Wang G. T.: Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments. J. Comput. Appl. Math. 236, 2425-2430 (2012).
17. Wang G. T., Agarwal R. P., Cabada A.: Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations. Appl. Math. Lett. 25, 1019-1024 (2012).
18. Wei Z. L., Dong W., Che J. L.: Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative. Nonlinear Anal. 73, 3232-3238 (2010).
19. Wei Z. L., Li Q. D., Che J. L.: Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative. J. Math. Anal. Appl. 367(1), 260-272 (2010).
20. Zhang, S. Q., Su, X. W.: The existence of a solution for a fractional differential equation with nonlinear boundary conditions considered using upper and lower solutions in reverse order, Comput. Math. Appl. (2011). doi: 10. 1016/j. camwa. 2011. 03. 008.
21. Zhang S. Q.: Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives. Nonlinear Anal. 71, 2087-2093 (2009).
22. Zhang S. Q.: Existence of a solution for the fractional differential equation with nonlinear boundary conditions. Comput. Math. Appl. 61, 1202-1208 (2011).
23. Zhang S. Q.: Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives. Nonlinear Anal. 71, 2087-2093 (2009).
24. Zhou Y.: Existence and uniqueness of fractional functional differential equations with unbounded delay. Int. J. Dyn. Syst. Differ. Equ. 1(4), 239-244 (2008).
25. Zhou Y.: Existence and uniqueness of solutions for a system of fractional differential equations. J. Frac. Calc. Appl. Anal. 12, 195-204 (2009).
26. Zhou Y., Jiao F.: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal. 11, 4465-4475 (2010).