Time distributed order two-sided space differential equations of arbitrary order offer a robust approach to modelling complex dynamical systems. In this study, we describe a scheme for obtaining the numerical solutions of time distributed order multidimensional two-sided space fractional differential equations. The numerical discretization scheme is a hybrid scheme, comprising a Newton-Cotes quadrature formula and a spectral collocation method. The time distributed order fractional differential

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... operator is approximated using the composite Simpson's rule, and the solution of the resulting differential equation is expressed as a linear combination of shifted Chebyshev polynomials in all variables. Convergence analysis of the numerical scheme is presented. Some one-and two-dimensional time distributed order two-sided space fractional differential equations, such as the fractional advection-dispersion and diffusion equations, are presented to demonstrate the accuracy and computational efficiency of the numerical scheme, and numerical solutions are compared with the exact solutions, where these are available.