Conformable Fractional Cosine Families of Operators
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^{...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Mahmut Akyigit
2019-08-01
|
| Series: | Journal of Mathematical Sciences and Modelling |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/805019 |
| _version_ | 1797350535113736192 |
|---|---|
| author | L. S. Chadli Said Melliani Elomari M'hamed |
| author_facet | L. S. Chadli Said Melliani Elomari M'hamed |
| author_sort | L. S. Chadli |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T12:46:16Z |
| format | Article |
| id | doaj.art-587ab7e8f02a44db8b70867cc3fa5103 |
| institution | Directory Open Access Journal |
| issn | 2636-8692 |
| language | English |
| last_indexed | 2024-03-08T12:46:16Z |
| publishDate | 2019-08-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj.art-587ab7e8f02a44db8b70867cc3fa51032024-01-21T07:04:09ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922019-08-012211211610.33187/jmsm.4354811408Conformable Fractional Cosine Families of OperatorsL. S. ChadliSaid MellianiElomari M'hamed0Laboratory of applied mathematics and scientific calculusIn 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.https://dergipark.org.tr/tr/download/article-file/805019$\alpha$-cosine familiesconformable derivativemild solution |
| spellingShingle | L. S. Chadli Said Melliani Elomari M'hamed Conformable Fractional Cosine Families of Operators Journal of Mathematical Sciences and Modelling $\alpha$-cosine families conformable derivative mild solution |
| title | Conformable Fractional Cosine Families of Operators |
| title_full | Conformable Fractional Cosine Families of Operators |
| title_fullStr | Conformable Fractional Cosine Families of Operators |
| title_full_unstemmed | Conformable Fractional Cosine Families of Operators |
| title_short | Conformable Fractional Cosine Families of Operators |
| title_sort | conformable fractional cosine families of operators |
| topic | $\alpha$-cosine families conformable derivative mild solution |
| url | https://dergipark.org.tr/tr/download/article-file/805019 |
| work_keys_str_mv | AT lschadli conformablefractionalcosinefamiliesofoperators AT saidmelliani conformablefractionalcosinefamiliesofoperators AT elomarimhamed conformablefractionalcosinefamiliesofoperators |