Conformable Fractional Cosine Families of Operators

Authors : Elomari M`HAMED, Said MELLİANİ, L S CHADLİ

Pages : 112-116

Doi:10.33187/jmsm.435481

View : 19 | Download : 14

Publication Date : 2019-08-30

Article Type : Research Paper

Abstract :In this paper we are concerned with the problem \begin{eqnarray*}\begin{cases} u^{insert ignore into journalissuearticles values(\alpha);}insert ignore into journalissuearticles values(t);=Auinsert ignore into journalissuearticles values(t);+finsert ignore into journalissuearticles values(t,uinsert ignore into journalissuearticles values(t););& t\in [0,T]\\ uinsert ignore into journalissuearticles values(0);=u_0, D^{\alpha}uinsert ignore into journalissuearticles values(0);=u_1\end{cases}\end{eqnarray*}  \begin{eqnarray*}     \begin{cases}     u^{insert ignore into journalissuearticles values(\alpha);}insert ignore into journalissuearticles values(t);=Auinsert ignore into journalissuearticles values(t);+finsert ignore into journalissuearticles values(t,uinsert ignore into journalissuearticles values(t););& t\in [0,T]\\     uinsert ignore into journalissuearticles values(0);=u_0, D^{\alpha}uinsert ignore into journalissuearticles values(0);=u_1     \end{cases}   \label{pb1} \end{eqnarray*}   Where $\alpha\in insert ignore into journalissuearticles values(1,2]$, and we use the conformable derivative. We give the notion of $\alpha$-Cosine families and proveded the existence and uniqueness of the problem 0.1.
Keywords : \alpha cosine families, Conformable derivative, Mild solution