On General Solution for Fractional Differential Equations with Not Instantaneous Impulses

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Zhang, Xianmin^{a; *; †} | Zhang, Xianzhen^b | Cao, Hui^c

Affiliations: [a] School of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, China. z6x2m@126.com | [b] School of Chemical and Environmental Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, China | [c] School of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, China

Correspondence: [†] Address for correspondence: School of Electronic Engineering, Jiujiang University, Jiujiang, Jiangxi 332005, China

Note: [*] The authors are deeply grateful to the anonymous referees for their kind comments, correcting errors and improving written language, which have been very useful for improving the quality of this paper

Abstract: In this paper we mainly study a kind of fractional differential equations with not instantaneous impulses, and find the equivalent equations of the impulsive system. The obtained result discovers that there exist general solution for the impulsive system. Next, an example is given to illustrate the obtained result.

Keywords: fractional differential equations, impulsive fractional differential equations, not instantaneous impulse, impulse, general solution

DOI: 10.3233/FI-2017-1497

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 355-369, 2017