documentclass{memoir}
usepackage[demo]{graphicx}
usepackage{amsmath}

newcommandlistequationname{List of Equations}
newlistof{listofequations}{equ}{listequationname}
newcommand{myequation}[1]{%
    addcontentsline{equ}{equation}{%
        protectnumberline{theequation} #1%
    }%
}


begin{document}
    frontmatter
    bgroup
      chapterstyle{article}
      tableofcontents
      listoffigures
      listoftables
      listofequations
    egroup

    mainmatter
    chapter{A chapter}
    section{A section}
        begin{figure}[htbp]
            caption{some figure caption}
        end{figure}
        begin{table}[htbp]
            caption{some table caption}
        end{table}
        begin{gather}
            y = mx + b label{eqn:linear}
        end{gather}myequation{Linear Equation}
end{document}

contentsline {table}{numberline {B.5}{ignorespaces Al SpeciesDiffision Coefficients}}{110}{table.caption.69}

contentsline {equation}{numberline {1.1}{ignorespaces Expression for Critical Cooing Rate, From Heat Capacity and Sample Size}}{10}{equation.1.1.1}

contentsline{figure}{...}
contentsline{table}{...}
contentsline{equation}{...}
contentsline{<ANY OTHER CUSTOM LISTING>}{...}