Existence results for fractional differential equations with infinite delay and interval impulsive conditions

Downloads

DOI:

https://doi.org/10.26637/mjm201/003

Abstract

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 theorem

Mathematics Subject Classification:

26A33, 34A08, 35R12, 47H10
  • A. Anguraj Department of Mathematics, P.S.G College of Arts and Science, Coimbatore- 641 014, Tamil Nadu, India.
  • M. Lathamaheswari Department of Mathematics, P.S.G College of Arts and Science, Coimbatore- 641 014, Tamil Nadu, India.
  • 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

  • NA

Metrics

PDF views
78
Jan 2014Jul 2014Jan 2015Jul 2015Jan 2016Jul 2016Jan 2017Jul 2017Jan 2018Jul 2018Jan 2019Jul 2019Jan 2020Jul 2020Jan 2021Jul 2021Jan 2022Jul 2022Jan 2023Jul 2023Jan 2024Jul 2024Jan 2025Jul 2025Jan 20268
|

Published

01-01-2014

How to Cite

A. Anguraj, and M. Lathamaheswari. “Existence Results for Fractional Differential Equations With Infinite Delay and Interval Impulsive Conditions”. Malaya Journal of Matematik, vol. 2, no. 01, Jan. 2014, pp. 16-23, doi:10.26637/mjm201/003.
K. Hilal, L. Ibnelazyz, K. Guida, Said Melliani (2019)
Recent Advances in Intuitionistic Fuzzy Logic Systems. Studies in Fuzziness and Soft Computing, 372, 251.
10.1007/978-3-030-02155-9_20