REA Press null REA Press3042-13303042-1330 REA Press https://doi.org/10.48313/uda.v2i1.50 Research Article Weak fuzzy complex numbers, Quadratic weak fuzzy complex equation, Weak fuzzy complex functions, Weak fuzzy complex differential equation, Initial value problem The second-order constant-coefficient linear homogeneous weak fuzzy complex differential equations (WFC-DEs) and initial value problems (WFC-IVPs)The second-order constant-coefficient linear homogeneous weak fuzzy complex differential equations (WFC-DEs) and initial value problems (WFC-IVPs) Razouk Lama Department of Mathematics, Latakia University (Tishreen), Latakia, Syria. Mahmoud Suliman Department of Mathematics, Latakia University (Tishreen), Latakia, Syria. Ali Mohamad Department of Mathematics, Latakia University (Tishreen), Latakia, Syria. 03 2025 13 03 2025 2 1 © 2025 REA Press 2025

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 The second-order constant-coefficient linear homogeneous weak fuzzy complex differential equations (WFC-DEs) and initial value problems (WFC-IVPs)

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.

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