Pseudoparabolic equations in matrix form

In this thesis, general integral representations are obtained for pseudoparabolic equation in matrix form L[w]:=w_{\overline \phi(z,t)+a(z)w(z,t)+b(z)\overline{w(z,t)}+c(z)w(z,t)+d(z)\overline{w(z,t)} which derived by generalized $Q$-holomorphic functions theory. Here $w(z,t)=\left\lbrace w_{ij}(z,t)\right\rbrace $ is an $m \times s$ complex valued matrix. The coefficients $a, b, c$ and $d$ are $m \times m$ complex matrix commuting with $Q$. Furthermore, the Riemann boundary value problem is defined by means of obtained integral representations and solutions to the problem are presented for non-negative index. The first section of the thesis is reserved for introduction and a summary of the literature is given. In the second section, information about the $ Q-$holomorphic functions which are to be used in later sections is given. In the following sections, obtained general solution representations for pseudoparabolic equation in matrix form which formed the subject of this thesis are given and solutions of Riemann boundary value problem are obtained for non-negative index.