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Second-order abstract Cauchy problem of conformable fractional type | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 94، دوره 13، شماره 2، مهر 2022، صفحه 1143-1150 اصل مقاله (378.53 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.20527.2163 | ||
| نویسندگان | ||
| Roshdi Khalil1؛ Sharifa Alsharif* 2؛ Sara Khamis3 | ||
| 1Department of Mathematics, Jordan University, Amman, Jordan | ||
| 2Department of Mathematics, Yarmouk University, Irbid, Jordan | ||
| 3Department of Mathematics, Lusail University, Doha, Qatar | ||
| تاریخ دریافت: 12 خرداد 1399، تاریخ بازنگری: 20 مرداد 1399، تاریخ پذیرش: 07 مهر 1399 | ||
| چکیده | ||
| In this paper, we discuss atomic solutions of the second-order abstract Cauchy problem of conformable fractional type \begin{eqnarray*} u^{(2\alpha )}(t)+Bu^{(\alpha )}(t)+Au(t) &=&f(t) \\ u(0) &=&u_{0}, \\ u^{(\alpha )}(0) &=&u_{0}^{(\alpha )}, \end{eqnarray*}% where $A,B$ are closed linear operators on a Banach space $X,$ $f$ $ :[0,\infty )\rightarrow X$ \ is continuous and $u$ is a continuously differentiable function on $[0,\infty )$. Some new results on atomic solutions using tensor product technique are obtained. | ||
| کلیدواژهها | ||
| Inverse problem؛ fractional derivative؛ tensor product of Banach spaces؛ atomic solution | ||
| مراجع | ||
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