Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701Second-order abstract Cauchy problem of conformable fractional type11431150632410.22075/ijnaa.2020.20527.2163ENRoshdi KhalilDepartment of Mathematics, Jordan University, Amman, JordanSharifa AlsharifDepartment of Mathematics, Yarmouk University, Irbid, JordanSara KhamisDepartment of Mathematics, Lusail University, Doha, QatarJournal Article20200601In this paper, we discuss atomic solutions of the second-order abstract Cauchy problem of conformable fractional type <br />\begin{eqnarray*}<br />u^{(2\alpha )}(t)+Bu^{(\alpha )}(t)+Au(t) &=&f(t) \\<br />u(0) &=&u_{0}, \\<br />u^{(\alpha )}(0) &=&u_{0}^{(\alpha )},<br />\end{eqnarray*}%<br />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.https://ijnaa.semnan.ac.ir/article_6324_b0e102726f7769291a90e2ef0da4df44.pdf