The second-order constant-coefficient linear homogeneous weak fuzzy complex differential equations (WFC-DEs) and initial value problems (WFC-IVPs) - Razouk, Lama; Mahmoud, Suliman; Ali, Mohamad (Uncertainty Discourse and Applications, 2025)
This work aims to introduce the concept of the second-order Weak Fuzzy Complex-Differential Equations (WFC-DEs) for the first time. A special isomorphic transformation function could write a WFC-DE as two related Differential Equations (DEs) of the second order concerning their real variables. We study the second-order constant-coefficient linear homogeneous DE in a Weak Fuzzy Complex (WFC) variable with WFC constant coefficients. Also, we study the simple form of this type of WFC-DE with real constant coefficients. Thus, to find the general solution, we use the characteristic equation of the second-order DE. Also, we get a particular solution for the second-order constant-coefficient linear homogeneous Weak Fuzzy Complex-Initial Value Problem (WFC-IVP). To enhance understanding, we provide illustrative examples for each problem discussed.