A Systematic Spectral-Tau Method for the Solution of Fuzzy Fractional Diffusion and Fuzzy Fractional Wave Equations

Abstract

In this paper, fuzzy fractional diffusion equations (FFDEs) and fuzzy fractional wave equations (FFWEs), subjected to initial and boundary conditions are considered. As these equations have significant applications in physics and engineering, a methodical spectral-tau scheme is utilized to obtain efficient solutions of FFDE and FFWE. For this purpose, shifted Chebyshev polynomials (SCPs) together with its operational matrix of integration in Riemann-Liouville sense and operation matrix of derivative in Caputo sense are employed to approximate the fuzzy-valued functions, their integral and differential terms, respectively. The proposed method is applied to some illustrative examples considered under generalized Hukuhara partial differentiability ($gH_{P}$-differentiability). Graphical results are included with error bar plots of each example that show the efficiency and convergence of the method towards the exact solution.