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In this article, the properties of single-term Walsh series are presented and utilized for solving the nonlinear Volterra-Hammerstein integral equations of second kind. The interval [0;1) is divided tomequal subintervals,mis a positive integer number. The midpoint of each subinterval is chosen as a suitable collocation point. By the method the computations of integral equations reduce into some nonlinear algebraic equations. The method is computationally attractive, and gives a continuous approximate solution. An analysis for the convergence of method is presented.The efficiency and accuracy of the method are demonstrated through illustrative examples. Some comparisons aremade with the existing results.

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In this article the Caputo time- and Riesz space-fractional Fokker-Planck equation (TSFFPE) is solved by the stable Gaussian radial basis function (RBF) method. By a spatial discretization and using the Riesz fractional derivative of the stable Gaussian radial basis function interpolants computed in [23], the computations of TSFFPE reduced to a system of fractional ODEs. A high order finite difference method is presented for this system of ODEs, and the computations are converted to a system of linear or nonlinear algebraic equations, in each time step. In the nonlinear case, these systems can be easily solved by the Newton iterative method. Numerical illustrations are performed to confirm the accuracy and efficiency of the presented method. Some comparisons are made with the results in other literature.