        TY  - JOUR
T1  - Conformable Fractional Cosine Families of Operators
AU  - M&#039;hamed, Elomari
AU  - Melliani, Said
AU  - Chadli, L. S.
PY  - 2019
DA  - August
Y2  - 2019
DO  - 10.33187/jmsm.435481
JF  - Journal of Mathematical Sciences and Modelling
PB  - Mahmut AKYİĞİT
WT  - DergiPark
SN  - 2636-8692
SP  - 112
EP  - 116
VL  - 2
IS  - 2
LA  - en
AB  - In this paper we are concerned with the problem \begin{eqnarray*}\begin{cases} u^{(\alpha)}(t)=Au(t)+f(t,u(t))&amp;amp; t\in [0,T]\\ u(0)=u_0, D^{\alpha}u(0)=u_1\end{cases}\end{eqnarray*} \begin{eqnarray*}   \begin{cases}   u^{(\alpha)}(t)=Au(t)+f(t,u(t))&amp;amp; t\in [0,T]\\   u(0)=u_0, D^{\alpha}u(0)=u_1   \end{cases}  \label{pb1} \end{eqnarray*}  Where $\alpha\in (1,2]$, 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.
KW  - $\alpha$-cosine families
KW  - Conformable derivative
KW  - Mild solution
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UR  - https://doi.org/10.33187/jmsm.435481
L1  - https://dergipark.org.tr/en/download/article-file/805019
ER  -