Existence of solutions for fuzzy fractional impulsive dynamic equations on time scale
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In this paper, we consider a class of fuzzy fractional impulsive dynamic equations on time scales of the form \begin{equation*} \begin{array}{lll} \delta_H^\alpha y(t)&=& p(t)\cdot y(t)+f(t, y(t)),\; t\in [0, T],\\ y(0)&=& y_0,\\ y(t_i^{+})&=& y(t_i^-)+I(t_i, y(t_i)),\; i\in \{1, \ldots, n\}.\\ \end{array} \end{equation*} Using Krasnosel$^\prime$skii and Sadovskii$^\prime$s fixed point theorems, we investigated and established the existence and uniqueness of solutions of this class of equations.
Abstract
In this paper, we consider a class of fuzzy fractional impulsive dynamic equations on time scales of the form \begin{equation*} \begin{array}{lll} \delta_H^\alpha y(t)&=& p(t)\cdot y(t)+f(t, y(t)),\; t\in [0, T],\\ y(0)&=& y_0,\\ y(t_i^{+})&=& y(t_i^-)+I(t_i, y(t_i)),\; i\in \{1, \ldots, n\}.\\ \end{array} \end{equation*} Using Krasnosel$^\prime$skii and Sadovskii$^\prime$s fixed point theorems, we investigated and established the existence and uniqueness of solutions of this class of equations.