Conformable Fractional Cosine Families of Operators

Year 2019, , 112 - 116, 30.08.2019

Elomari M'hamed , Said Melliani L. S. Chadli

https://doi.org/10.33187/jmsm.435481

Abstract

In this paper we are concerned with the problem \begin{eqnarray*}\begin{cases} u^{(\alpha)}(t)=Au(t)+f(t,u(t))& 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))& 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.

Keywords

$\alpha$-cosine families, Conformable derivative, Mild solution

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