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Purpose – In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution. Design/methodology/approach – The methodology is based on the geometric function theory. Findings – The authors present a new analytic function for a class of complex LDEs. Originality/value – The authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.