Analytical Solution of Linear Second-Order Non-Homogeneous Fuzzy Partial Differential Equations Using The Fuzzy Sumudu Transform Under Generalized Hukuhara Differentiability
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Keywords:
Strongly Generalized Hukuhara Differentiability; Fuzzy Sumudu Transform; Initial and Boundary Conditions; Non-Linear Differential Equation; Non-Homogeneous Fuzzy Partial Differential Equation.Abstract
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.
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