D-stability of the model of the Stieltjes string related to the functional differential equations

The following model $p\left(t\right)u^{\prime }\left(t\right)-p\left(0\right)\beta -{\int }_0^t\left(\left(gu\right)\left(s\right)+\sum _{i=1}^m\left({\xi }_i\left(s\right)x\left({\nu }_i\left(s\right)\right)-{\psi }_i\left(s\right)x\left({\mu }_i\left(s\right)\right)\right)\right)dQ\left(s\right)=-F\left(t\right)$of the Stieltjes string on the segment $[0,l]$ with a nonlocal initial value condition $u\left(0\right)=\alpha$ is considered. $D$-stability conditions of the unique solution of the mentioned problem are established. Also, example is presented.