A Comprehensive Study on Exact and Numerical Methods for Solving the Neutrosophic Fuzzy Advection–Diffusion Equation

In this article, an in‐depth study of the advection–diffusion equation in a neutrosophic fuzzy environment is discussed for the first time in the literature, including truth (T), indeterminacy (I), and falsehood (F) fuzzy components. Furthermore, analytical and numerical methods that are Galilean transformation and explicit finite difference methods are reformulated, developed, and applied for solving the neutrosophic fuzzy advection–diffusion equation. The neutrosophic triangular number concept was utilized for both neutrosophic numerical and exact solutions. The error bound between the neutrosophic numerical and exact solution evaluated at the ( α , β , γ )‐cut level set is illustrated and evaluated. Finally, a numerical example is solved using both analytical and numerical techniques, and the results indicate the effectiveness and feasibility of the proposed developed methods.