Existence of Solutions to Anti-periodic Boundary Value Problem for Nonlinear Fractional Differential Equations

Differential Equations and Dynamical Systems

Volumn 19, Issue 3, 2011, Pages 237-252

  Chen, Anping ^a,b   Chen, Yi ^b  

^a XIANGNAN UNIVERSITY   (China)

^b XIANGTAN UNIVERSITY   (China)

Author keywords

Anti periodic boundary value problem; Fixed point theorem; Fractional differential equation

Indexed keywords

EID: 84859725749     PISSN: 09713514     EISSN: 09746870     Source Type: Journal    
DOI: 10.1007/s12591-011-0086-2     Document Type: Article

References (18)

1. Kilbas A. A., Srivastava H. M., Trujillo J. J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).
2. Aftabizadeh R., Huang Y. K., Pavel N. H.: Nonlinear third-order differential equations with anti-periodic boundary conditions and some optimal control problems. J. Math. Anal. Appl. 192(1), 266-293 (1995).
3. Ahmad, B., Espinar, V. O.: Existence of solutions for fractional differential inclusions with antiperiodic boundary conditions, boundary value problems. (2009). doi: 10. 1155/2009/625347.
4. Ahmad B.: Existence of solutions for fractional differntial equations of order q ∈ (2,3] with anti-periodic boundary conditions. J. Appl. Math. Comput 34(1-2), 385-391 (2009).
5. Bai Z., Lü H.: Positive solutions for boundary value problem of nonlinear fractional differential equations. J. Math. Anal. Appl. 311(2), 495-505 (2005).
6. Franco D., Nieto J. J., O'Regan D.: Anti-periodic boundary value problem for nonlinear first order ordinary differential equations. Math. Inequal. Appl. 6, 477-485 (2003).
7. Fan Q. Y., Wang W. T., Yi X. J.: Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays. J. Comput. Appl. Math. 230(2), 762-769 (2009).
8. Jankowski T.: Ordinary differential equations with anti-periodic and nonlinear boundary value conditions of anti-periodic type. Comput. Math. Appl. 47(8-9), 1429-1436 (2004).
9. Lakshmikantham V., Leela S., Vasundhara D. J.: Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009).
10. Li C. F., Luo X. N., Zhou Y.: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. Comput. Math. Appl. 59(3), 1363-1375 (2010).
11. Miller K. S., Ross B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993).
12. Podlubny I.: Fractional Differential Equations, Mathematics in Science and Engineering. Academic Press, New York (1999).
13. Samko S. G., Kilbas A. A., Marichev O. I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon (1993).
14. Tian, Y., Chen, A.: The existence of positive solution to three-point singular boundary value problem of fractional differential equation. Abstr. Appl. Anal. (2009). doi: 10. 1155/2009/314656.
15. Wang W. B., Shen J. H.: Existence of solutions for anti-periodic boundary value problems. Nonlinear Anal. 70(2), 598-605 (2009).
16. Yin Y.: Remarks on first order differential equations with anti-periodic and nonlinear boundary value conditions. Nonlinear Times Digest. 2, 83-94 (1995).
17. Yin Y.: Monotone iterative technique and quasilinearization for some anti-periodic problem. Nonlinear World 3, 253-266 (1996).
18. Zhang S. Q.: Positive solutions for boundary value problem of nonlinear fractional differential equations. Electr. J. Differ. Equ 36, 1-12 (2006).