Fuzzy fractional diffusion equation with time delay having power law and Mittag-Leffler kernel

In this article, we study a new type of mathematical model of the diffusion equation. This model has space and time-fractional derivative with both singular and non-singular derivative i.e., having power-law kernel and Mittag-Leffler kernel. This model is taken in a fuzzy environment. A delay term is also added to this model. First, we approximate the unknown fuzzy function as a truncated series expansion of shifted Chebyshev polynomials. We find an approximate formula for fractional derivatives and delay function. The main advantage of this method in applying this method is, the taken fuzzy fractional partial differential equation (FFPDE) reduces into a system of a non-linear fuzzy algebraic equation. We solve this system by any method available in the literature and find the value of unknowns. We depict the validity and feasibility of this derived method by deriving numerical solution of particular cases of taken fuzzy model. We observe that this method is valid for a fuzzy fractional differential equation with delay term and has good accuracy as seen from the error tables.