@article{Lopushansky_Lopushanska_2022, title={Inverse problem with two unknown time-dependent functions for $2b$-order differential equation with fractional derivative}, volume={14}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/5228}, DOI={10.15330/cmp.14.1.213-222}, abstractNote={<p>We study the inverse problem for a differential equation of order $2b$ with a Riemann-Liouville fractional derivative over time and given Schwartz-type distributions in the right-hand sides of the equation and the initial condition. The generalized (time-continuous in a certain sense) solution $u$ of the Cauchy problem for such an equation, the time-dependent continuous young coefficient and a part of a source in the equation are unknown.</p> <p>In addition, we give the time-continuous values $\Phi_j(t)$ of desired generalized solution $u$ of the problem on a fixed test functions $\varphi_j(x)$, $x\in \mathbb R^n$, namely $(u(\cdot,t),\varphi_j(\cdot))=\Phi_j(t)$, $t\in [0,T]$, $j=1,2$.</p> <p>We find sufficient conditions for the uniqueness of the generalized solution of the inverse problem throughout the layer $Q:=\mathbb R^n\times [0,T]$ and the existence of a solution in some layer $\mathbb R^n\times [0,T_0]$, $T_0\in (0,T]$.</p>}, number={1}, journal={Carpathian Mathematical Publications}, author={LopushanskyA.O. and LopushanskaH.P.}, year={2022}, month={Jun.}, pages={213-222} }