A Solution of an Intuitionistic Fuzzy Time-Fractional Diffusion Equation Using a Modified Explicit Finite Difference Scheme

The utilization of fuzzy fractional partial differential equations has turned into a practical tool for modeling real-life phenomena because they offer a compact framework for modeling complex phenomena with uncertainty, providing insights and reflecting on systems that classical models cannot adequately get. In this paper, the intuitionistic fuzzy time-fractional diffusion equation is investigated where the parameters and variables are deemed as intuitionistic fuzzy numbers. A modified explicit finite difference scheme is formulated and applied for solving the intuitionistic fuzzy time-fractional diffusion equation. The stability of the proposed scheme is discussed using the von Neumann method. The nonmembership and membership functions are employed to get characteristic properties on the standard r-cut and β-cut of the fuzzy intuitionistic numerical solutions. The fuzzification process of deterministic r-cut and β-cut solutions leads to the fuzzy intuitionistic numerical solution. Lastly, a numerical example is given to demonstrate and illustrate the presented method and to investigate specific related aspects. The study indicated that the results obtained are in strong agreement with the theoretical predictions. Hence, the presented modified explicit is well suited for solving intuitionistic fuzzy time-fractional diffusion equations.