Response to 'Comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19:401-3.]'

摘要

This paper is a response to "Comments on the concept of existence of solution for impulsive fractional differential equations" by Wang et al. (2014) [1]. Recently, Wang et al. (2014) [1] made some comments on our paper (Feckan et al., 2012) [2] and claimed that "The objective of this note to indicate the mistake in these counterexamples and show the plausibility of the previous results". To achieve their aim, they used classical Caputo fractional derivative and changed it in each subintervals by keeping the impulses which start the lower bounded from different impulsive points. However, we (Feckan et al., 2012) [2] mean a different one, generalized Caputo derivative, by keeping in each impulses which start the lower bounded from zero. In support of our view-points, we present some scripts to address and discuss the comments.