3rd TAGRA

Non-Newtonian calculus offers alternative frameworks for studying functions with different analytical structures. This study presents a first-order local approximation method for mixed-type functions containing classical and non-Newtonian components. In the proposed method, each component is approximated within its corresponding calculus, and the resulting approximations are combined according to the structure of the original function. The method is applied to a function containing exponential and double-exponential components. Its local behavior is compared with that of the classical first-order Taylor approximation through absolute and relative error analysis. In the example examined, the proposed method produces smaller approximation errors near the expansion point. This finding suggests that retaining the structure of the individual components can improve the local representation of mixed-type functions.