TY - JOUR
ID - 6324
TI - Second-order abstract Cauchy problem of conformable fractional type
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Khalil, Roshdi
AU - Alsharif, Sharifa
AU - Khamis, Sara
AD - Department of Mathematics, Jordan University, Amman, Jordan
AD - Department of Mathematics, Yarmouk University, Irbid, Jordan
AD - Department of Mathematics, Lusail University, Doha, Qatar
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 1143
EP - 1150
KW - Inverse problem
KW - Fractional derivative
KW - tensor product of Banach spaces
KW - atomic solution
DO - 10.22075/ijnaa.2020.20527.2163
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_6324.html
L1 - https://ijnaa.semnan.ac.ir/article_6324_b0e102726f7769291a90e2ef0da4df44.pdf
ER -