@article{article_503761, title={Generalized solution of boundary value problem with an inhomogeneous boundary condition}, journal={MANAS Journal of Engineering}, volume={7}, pages={157–165}, year={2019}, author={Abdyldaeva, Elmira and Taalaibek Kyzy, Gulbarchyn and Anarkulova, Bermet}, keywords={Boundary value problem,Boundary control conditıon,Generalized solution,İntegral equation,Fourier series}, abstract={<table class="MsoNormalTable" border="0" cellspacing="0" cellpadding="0" width="627" style="width:470.3pt;"> <tbody> <tr> <td width="530" valign="top" style="width:397.4pt;padding:0in 5.4pt;"> <div style="border:none;border-top:solid #000000 1pt;padding:1pt 0in 0in 0in;"> <p class="MsoNormal" style="text-align:justify;line-height:150%;border:none;padding:0in;"> <span style="font-size:12pt;line-height:150%;">In this problem, we study the solution to boundary value problem for a controlled oscillation process, described by Fredholm integro-differential equation with an inhomogeneous boundary condition. An algorithm is developed for constructing a generalized solution of boundary value problem. It is proved that a weak generalized solution is an element of Hilbert space. Approximate solutions of the boundary value problem are determined and their convergence is proved. </span> <span lang="ky" style="font-size:12pt;line-height:150%;" xml:lang="ky"> </span> </p> <p> </p> <p class="MsoNormal" style="text-align:justify;line-height:150%;border:none;padding:0in;"> <span lang="ky" style="font-size:12pt;line-height:150%;" xml:lang="ky"> </span> </p> <p>  </p> </div> </td> </tr> </tbody> </table>}, number={2}, publisher={Kyrgyz-Turkish Manas University} }