Abstract
In this present article, a model of the fractional diffusion equation in a fuzzy environment is studied with both singular and nonsingular kernels with a Mittag-Leffler kernel. In this model, initial boundary conditions and coefficients are fuzzy numbers. First ofall, we derive the Legendre operational matrix of fractional differentiation concerning the power kernel and Mittag-Leffler kernel. We used the spectral method in addition to these derived operational matrices to find out the numerical solution of the taken model. This method is easily applicable to fuzzy partial differential equation (PDE) with different fractional operators. It reduced the given model into algebraic equations, which with further solving gives the solution of the model. The feasibility and accuracy of the method on a fractional fuzzy PDE can be seen through the numerical examples in which we incorporated the error table calculated between exact and numerical solution. The dynamics of the model concerning different parameters present in the model are presented in thorough figures. The application of this model in porous media is presented.
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