- Results in Nonlinear Analysis
- Volume:1 Issue:3
- Existence Results for Nonautonomous Impulsive Fractional Evolution Equations
Existence Results for Nonautonomous Impulsive Fractional Evolution Equations
Authors : Dimplekumar CHALİSHAJAR, Duraisamy Senthil RAJA, Kulandhaivel KARTHİKEYAN, Ponnusamy SUNDARARAJAN
Pages : 133-147
View : 32 | Download : 11
Publication Date : 2018-11-14
Article Type : Research Paper
Abstract :\noindent {\bf ABSTRACT} \end{center} \par In this paper, we investigate the mild solutions of a nonlocal Cauchy problem for nonautonomous fractional evolution equations \begin{align*} \begin{cases} \frac{d^q uinsert ignore into journalissuearticles values(t);}{dt^q} &\quad =~~ -Ainsert ignore into journalissuearticles values(t);uinsert ignore into journalissuearticles values(t);+finsert ignore into journalissuearticles values(tinsert ignore into journalissuearticles values(K_1 u);insert ignore into journalissuearticles values(t); insert ignore into journalissuearticles values(K_2 u);insert ignore into journalissuearticles values(t);,\dotsinsert ignore into journalissuearticles values(K_n u);insert ignore into journalissuearticles values(t);,t \in I=[0,T] \\ \Delta y|_{t=t_k} &\quad =~~ I_kinsert ignore into journalissuearticles values(yinsert ignore into journalissuearticles values(t_k^-););,t = t_k, k = 1,2,\dots,m, \\ uinsert ignore into journalissuearticles values(0); &\quad =~~ A^{-1}insert ignore into journalissuearticles values(0);ginsert ignore into journalissuearticles values(u);+u_0 \end{cases} \end{align*} in Banach spaces, where $T>0, 0ORIGINAL ARTICLE URL