A Solution of Fuzzy Time Fractional Wave Equation via Two Modified Implicit Finite Difference Schemes

Fuzzy fractional partial differential equations have become a powerful approach for handling uncertainty or imprecision in real-world modeling problems.In this study, two finite difference schemes, the Crank-Nicolson and centered-time centered-space methods, were developed and used to obtain a numerical solution for double-parametric fuzzy time fractional wave equations.Fuzzy set theory principles were employed to perform fuzzy analysis and formulate the proposed numerical schemes.The Caputo formula was used to define the time-fractional derivative.To illustrate the practicality of the numerical method, a specific numerical instance was analyzed.The results are presented in tables and figures, revealing the efficacy of the schemes in terms of accuracy and ability to reduce computational expenses.A novel fuzzy computational approach known as the double-parametric form enabled these achievements.