Abstract
This paper is concerned with the anti-periodic boundary value problem for nonlinear fractional differential equation. By means of the Banach fixed point theorem and Schauder fixed point theorem, some existence results are obtained.
Similar content being viewed by others
References
Kilbas A.A., Srivastava H.M., Trujillo J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
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)
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
Ahmad B.: Existence of solutions for fractional differntial equations of order \({q \in (2, 3]}\) with anti-periodic boundary conditions. J. Appl. Math. Comput 34(1–2), 385–391 (2009)
Bai Z., Lü H.: Positive solutions for boundary value problem of nonlinear fractional differential equations. J. Math. Anal. Appl. 311(2), 495–505 (2005)
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)
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)
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)
Lakshmikantham V., Leela S., Vasundhara D.J.: Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009)
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)
Miller K.S., Ross B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)
Podlubny I.: Fractional Differential Equations, Mathematics in Science and Engineering. Academic Press, New York (1999)
Samko S.G., Kilbas A.A., Marichev O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon (1993)
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
Wang W.B., Shen J.H.: Existence of solutions for anti-periodic boundary value problems. Nonlinear Anal. 70(2), 598–605 (2009)
Yin Y.: Remarks on first order differential equations with anti-periodic and nonlinear boundary value conditions. Nonlinear Times Digest. 2, 83–94 (1995)
Yin Y.: Monotone iterative technique and quasilinearization for some anti-periodic problem. Nonlinear World 3, 253–266 (1996)
Zhang S.Q.: Positive solutions for boundary value problem of nonlinear fractional differential equations. Electr. J. Differ. Equ 36, 1–12 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, A., Chen, Y. Existence of Solutions to Anti-periodic Boundary Value Problem for Nonlinear Fractional Differential Equations. Differ Equ Dyn Syst 19, 237–252 (2011). https://doi.org/10.1007/s12591-011-0086-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12591-011-0086-2