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Variable-order time fractional Volterra–Fredholm integral partial differential equations with weakly singular kernels are taken into account as results of modeling diverse physical phenomena. In order to determine the approximate solution of this category of functional equation, a matrix collocation method by utilizing the hybrid Bernstein polynomials and block-pulse functions is proffered so that their two-dimensional operational matrices of the integration are derived to avoid the integration operation. Therefore, the speed of computations will increase. Convergence, error estimation, existence and uniqueness of the solution are inspected. The approach discussed is executed on several experimental examples and the results illustrate the effectiveness, applicability and accuracy of the proposed method.
Rostami et al. (Sun,) studied this question.