Bianchi type-III non-static magnetized cosmological model for perfect fluid distribution in general relativity

We have investigated Bianchi type III non-static magnetized cosmological model for perfect fluid distribution in general relativity. We assume that F12 is the only non-vanishing component of Fij. Maxwell’s equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\partial}{\partial {x}^{j}}\bigl(F_{{ij}}\sqrt{-g}\bigr)=0$$\end{document} leads to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{12}=\mathrm{Ke}^{-\alpha {x}}$$\end{document} where K and α are constants.