Abstract
In this paper, we discuss some existence results for a class of multi-point boundary value problem for impulsive fractional functional differential equations. Some sufficient conditions are obtained by using suitable fixed point theorems. Examples are also given to illustrate our results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agarwal, R.P., Andrade, B., Cuevas, C.: Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations. Nonlinear Anal., Real World Appl. 11, 3532–3554 (2010)
Agarwal, R.P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109, 973–1033 (2010)
Agarwal, R.P., Lakshmikantham, V., Nieto, J.J.: On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. 72, 2859–2862 (2010)
Ahmad, B.: Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations. Appl. Math. Lett. 23, 390–394 (2010)
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, 1838–1843 (2009)
Ahmad, B., Sivasundaram, S.: Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations. Nonlinear Anal. 3, 251–258 (2009)
Ahmad, B., Sivasundaram, S.: Existence of solutions for impulsive integral boundary value problems of fractional order. Nonlinear Anal., Hybrid Syst. 4, 134–141 (2010)
Bai, C.: Existence of positive solutions for boundary value problems of fractional functional differential equations. Electron. J. Qual. Theory Differ. Equ. 30, 1–14 (2010)
Balachandran, K., Kiruthika, S.: Existence of solutions of abstract fractional impulsive semilinear evolution equations. Electron. J. Qual. Theory Differ. Equ. 4, 1–12 (2010)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
Mophou, G.M.: Existence and uniqueness of mild solutions to impulsive fractional differential equations. Nonlinear Anal. 72, 1604–1615 (2010)
Smart, D.R.: Fixed Point Theorems. Cambridge University Press, Cambridge (1974)
Tian, Y., Bai, Z.: Existence results for the three-point impulsive boundary value problem involving fractional differential equations. Comput. Math. Appl. 59, 2601–2609 (2010)
Wang, G., Ahmad, B., Zhang, L.: Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order. Nonlinear Anal. 74, 792–804 (2011)
Zeidler, E.: Nonlinear Functional Analysis and Its Applications, I. Fixed-Point Theorem. Springer, New-York (1993)
Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Differ. Equ. 36, 1–12 (2006)
Zhou, Y., Jiao, F., Li, J.: Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71, 3249–3256 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, H. Existence results for fractional functional differential equations with impulses. J. Appl. Math. Comput. 38, 85–101 (2012). https://doi.org/10.1007/s12190-010-0465-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-010-0465-9