Chebyshev spectral method for variable-order fuzzy fractional advection diffusion equation by using Mittag-Leffler law
Keywords:
Fuzzy Calculus, Variable Order ABC Derivatives, Fuzzy PDEs, Diffusion EquationAbstract
In this paper we have proposed an efficient shifted fifth-kind Chebyshev spectral collocation method in solving nonlinear variable-order fuzzy fractional partial differential equations with Atangana–Baleanu–Caputo (ABC) fractional derivative with non-singular Mittag–Leffler kernel. Our model would include fuzzy-valued coefficients, source terms and initial and boundary conditions; by doing so we can model uncertainty and memory effects simultaneously. Through generalized Hukuhara differentiability and parametric fuzzy calculus fuzzy-valued functions are approximated by shifted fifth-kind Chebyshev polynomials and we derived a new variable order ABC operational matrix. The nonlinear fuzzy fractional reaction–advection–diffusion equation is then solved efficiently by a system of nonlinear algebraic equations. We consider three benchmark problems to validate our method. The numerical results show excellent agreement with analytical solutions, rapid spectral convergence and very small approximation errors while preserving the convexity and parametric properties of fuzzy solutions.
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