This　article　discusses　the　utilisation　of　a　Chua　oscillator　with　a　memristor　to　produce　chaos　with　minimal　nonlinearity.　The　memristor,　a　device　that　changes　its　flux　or　charges　over　time,　has　its　nonlinear　strength　altered　fractionally　to　determine　the　lowest-order　memristor　nonlinearity　for　generating　chaos.　An　experimental　analog　circuit　in　real-time　has　been　constructed.　A　linear　parameter　varying　(LPV)　approach,　incorporating　a　suitable　Lyapunov　functional　(LK)　method,　has　been　introduced　to　find　new　sufficient　conditions　for　the　robust　stability　of　the　resulting　closed-loop　system　through　linear　matrix　inequalities　(LMIs).　By　observing　the　behaviour　of　the　system　without　control,　it　is　possible　to　understand　the　basic　characteristics　of　chaotic　oscillations　and　how　they　are　affected　by　changes　in　the　fractional　order.　These　results　can　then　be　used　as　a　starting　point　to　study　the　effectiveness　of　various　control　techniques,　such　as　feedback　control,　in　reducing　chaos　and　stabilising　the　system　of　this　article.　The　efficiency　of　the　cost-function-based　control　scheme　is　evaluated　using　the　simulation　results　and　relevant　applications　are　addressed.