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J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2020,4]]},"abstract":"<jats:p> In this work, we develop a finite difference\/finite element method for the two-dimensional distributed-order time-space fractional reaction\u2013diffusion equation (2D-DOTSFRDE) with low regularity solution at the initial time. A fast evaluation of the distributed-order time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials. The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed. For the spatial approximation, the finite element method is employed. The convergence of the corresponding fully discrete scheme is investigated. 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