Analytical Solution of Linear Second-Order Non-Homogeneous ‎Fuzzy Partial Differential Equations Using The Fuzzy Sumudu ‎Transform Under Generalized Hukuhara Differentiability

In this paper, a linear second-order non-homogeneous fuzzy partial differential equation (FPDE) is constructed, and the Fuzzy Sumudu ‎Transform (FST) method is applied to solve FPDEs within the context of generalized Hukuhara(gH) differentiability technique. The use ‎of FST, a potent integral transform renowned for its scale-invariant and unit-preserving characteristics, to the fuzzy setting is expanded. ‎FPDEs are solved analytically by transforming them into more straightforward algebraic differential equations in the transform domain, ‎utilizing recent advances in the gH-differentiability technique. Initially, the basic characteristics of linear second-order non-homogeneous FPDEs are presented. To highlight the capabilities, a numerical example is provided.