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A NOTE ON LINEAR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS
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 Title & Authors
A NOTE ON LINEAR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS
Choi, Sung Kyu; Koo, Namjip;
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 Abstract
This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.
 Keywords
impulsive fractional differential equation;fractional integral inequality;Caputo fractional derivative;Mittag-Leffler function;
 Language
English
 Cited by
1.
ON EXACT SOLUTIONS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH NON-INTEGER ORDERS,;;

충청수학회지, 2016. vol.29. 3, pp.515-521 crossref(new window)
1.
ON EXACT SOLUTIONS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH NON-INTEGER ORDERS, Journal of the Chungcheong Mathematical Society, 2016, 29, 3, 515  crossref(new windwow)
 References
1.
S. K. Choi, B. Kang, and N. Koo, Stability for Caputo fractional differential equations, Proc. Jangjeon Math. Soc. 16 (2013), 165-174.

2.
S. K. Choi, B. Kang, and N. Koo, Stability of Caputo fractional differential systems, Abstr. Appl. Anal. 2014 (2014), Article ID 631419, 6 pages.

3.
S. K. Choi, N. Koo, and C. Ryu, Impulsive integral inequalities with a non-separable kernel, J. Chungcheong Math. Soc. 27 (2014), 651-659. crossref(new window)

4.
Z. Denton and A. S. Vatsala, Fractional integral inequalities and applications, Comput. Math. Appl. 59 (2010), 1087-1094. crossref(new window)

5.
M. Feckan, Y. Zhou, and J. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commmun Nonlinear Sci Numer Simulat. 17 (2012), 3050-3060. crossref(new window)

6.
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

7.
V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publishing Co. Pte. Ltd., NJ, 1989.

8.
V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers Ltd, 2009.

9.
G. M. Mittag-Leffler, Sur l'integrable de Laplace-Abel, C. R. Acad. Sci. Paris (Ser. II) 136 (1903), 937-939.

10.
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.

11.
J. Wang, Y. Zhou, and M. Feckan, Nonlinear impulsive problems for fractional di erential equations and Ulam stability, Comput. Math. Appl. 64 (2012), 3389-3405. crossref(new window)

12.
H. Ye, J. Gao, and Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equations J. Math. Anal. Appl. 328 (2007), 1075-1081. crossref(new window)