Browse > Article
http://dx.doi.org/10.14403/jcms.2016.29.3.515

ON EXACT SOLUTIONS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH NON-INTEGER ORDERS  

Choi, Sung Kyu (Department of Mathematics Chungnam National University)
Koo, Namjip (Department of Mathematics Chungnam National University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.3, 2016 , pp. 515-521 More about this Journal
Abstract
This paper deals with linear impulsive differential equations with non-integer orders. We provide the explicit representation of solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions.
Keywords
linear impulsive fractional differential equation; Caputo fractional derivative; Mittag-Leffler function;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
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.   DOI
4 S. K. Choi and N. Koo, A note on linear impulsive fractional differential equations, J. Chungcheong Math. Soc. 28 (2015), 583-590.   DOI
5 Z. Denton and A. S. Vatsala, Fractional integral inequalities and applications, Comput. Math. Appl. 59 (2010), 1087-1094.   DOI
6 M. Fe.ckan, Y. Zhou, and J. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commun Nonlinear Sci Numer Simulat. 17 (2012), 3050-3060.   DOI
7 A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
8 V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publishing Co. Pte. Ltd., NJ, 1989.
9 V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers Ltd, 2009.
10 V. D. Mil'man and A. D. Myshkis, On the stability of motion in the presence of impulses, Siberian Mathematical Journal 1 (1960), 233-237.
11 G. M. Mittag-Leffer, Sur l'integrable de Laplace-Abel, C. R. Acad. Sci. Paris (Ser. II) 136 (1903), 937-939.
12 J. Peng and K. Li, A note on property of the Mittag-Leffer function J. Math. Anal. Appl. 370 (2010), 635-638.   DOI
13 I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
14 J. Wang, Y. Zhou, and M. Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl. 64 (2012), 3389-3405.   DOI