International Journal of Nonlinear Analysis and Applications

Second-order abstract Cauchy problem of conformable fractional type

Document Type : Research Paper

Authors

1 Department of Mathematics, Jordan University, Amman, Jordan

2 Department of Mathematics, Yarmouk University, Irbid, Jordan

3 Department of Mathematics, Lusail University, Doha, Qatar

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 1143-1150
  • Receive Date: 01 June 2020
  • Revise Date: 10 August 2020
  • Accept Date: 28 September 2020