As　fossil　fuels　decline　on　a　global　scale,　there　is　a　rising　interest　in　developing　a　cost-effective　process　for　producing　biodiesel　from　renewable　sources,　like　Jatropha　curcas　plant.　Enzymatic　transesterification　of　Jatropha　oil　with　alcohol　is　an　effective　technique　to　produce　biodiesel.　Due　to　mass　transfer　limitation　between　Jatropha　oil　and　alcohol,　the　reaction　is　very　slow.　To　overcome　this　we　have　used　ultrasound　frequency　for　excessive　production　of　biodiesel.　This　article　examines　the　impact　of　ultrasound　frequency　on　the　enzymatic　transesterification　of　Jatropha　oil　through　a　mathematical　model.　Optimal　control　theory　through　Pontryagin　Minimum　Principle　is　employed　on　ultrasound　to　optimize　frequency　and　improve　cost-effectiveness　of　the　system.　The　model’s　validity　is　confirmed　through　simulated　results　and　comparison　with　experimental　data　from　the　literature.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.　2025.