Existence results for fractional differential equations with infinite delay and interval impulsive conditions
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DOI:
https://doi.org/10.26637/mjm201/003Abstract
This paper is mainly concerned with the existence and uniqueness of mild solutions for nonlocal fractional infinite delay differential equations with interval impulses. The results are obtained by using fixed point theorem.
Keywords:
Fractional derivative, fractional differential equations, impulsive conditions, fixed point theoremMathematics Subject Classification:
26A33, 34A08, 35R12, 47H10- Pages: 16-23
- Date Published: 01-01-2014
- Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)
A. Anguraj, P. Karthikeyan and GM. N’Guerkata, Nonlocal cauchy problem for some fractional abstract integro-differential equations in Banach spaces, Communications in Mathematical Analysis, 6(1)(2009), 31–35.
A. Anguraj, K. Karthikeyan and Y.-K. Chang, Existence for impulsive neutral integrodifferential inclusions with nonlocal initial conditions via fractional operators Nonlinear Analysis: Theory Methods and Applications, 71(2009), 4377–4386. DOI: https://doi.org/10.1016/j.na.2009.02.121
K. Balachandran and J.J. Trujillo, The non local Cauchy problem for nonlinear fractional integrodifferential equations in Banach Spaces, Nonlinear Analysis: Theory Methods and Applications, 72(2010), 4587-4593. DOI: https://doi.org/10.1016/j.na.2010.02.035
K. Balachandran, S. Kiruthika and J.J. Trujillo, Existence results for fractional impulsive integrodifferential equations in Banach spaces, Communications in Nonlinear Science and Numerical Simulation, 16(4)(2011), 1970-1977. DOI: https://doi.org/10.1016/j.cnsns.2010.08.005
M. Benchohra and B.A. Slimani, Existence and Uniqueness of solutions to impulsive fractional differential equations, Electronic Journal of Differential Equations, 2009:2009(10), 1–11. DOI: https://doi.org/10.14232/ejqtde.2009.4.8
E. Hernadez and Donal O’Regan, On a new class of abstract impulsive differential equations, Proceedings of American Mathematical Society, (pre-print).
A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, in: North - Holland Mathematics Studies, Vol.204, Elsevier, Amsterdam, 2006.
V. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, 2009.
V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations. World Scientific, Singapore, 1989. DOI: https://doi.org/10.1142/0906
R.H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Robert E. Krieger Publ. Co., Florida, 1987.
K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1993.
A. Samoilenko and M. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. DOI: https://doi.org/10.1142/2892
X. Zhang, X. Huang and Z. Liu, The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay, Nonlinear Analysis: Hybrid Systems, 4 (2010), 775–781. DOI: https://doi.org/10.1016/j.nahs.2010.05.007
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