Recently,　different　neural　network　models　and　synapse　models　have　been　introduced　by　significant　laboratories　worldwide.　The　research　on　mem-elements　is　a　promising　branch　of　research　due　to　their　natural　symmetry　with　synapses.　Nevertheless,　neuromorphic　computing　with　memcapacitor　is　still　in　its　infancy,　especially　when　fractional-order　memcapacitor　is　considered.　Fractional-order　memcapacitor　bridge　synapse-based　neural　network　and　its　dynamic　behavior　are　utterly　uncharted　territory.　The　mode　of　action　in　the　synaptic　dynamical　state　and　topological　structure　of　the　neural　network　needs　to　be　thoroughly　analyzed.　This　paper　shows　the　saturation　process　of　fractional-order　memcapacitor　bridge　synapse　by　using　a　general　fractional-order　memcapacitor　model.　The　role　of　fractional-order　in　the　dynamic　transformation　of　neural　network　weights　is　discussed.　The　influence　of　fractional-order　is　quantitatively　analyzed,　and　a　kind　of　simple　neural　network　circuit　topology　is　proposed.　©　2022　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.