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Maxwell model is one of the most outstanding and widely used models for the description of viscoelastic materials. In this study, we use an efficient meshfree technique based on the Moving Kriging (MK) interpolation for the numerical solution of Magnetohydrodynamic (MHD) flow of fractional Maxwell fluid. In this scheme to discretize this equation in time and space variables, we use the finite difference method and MK interpolation shape functions, respectively. Also, we calculate the local weak form for every node instead of the computation of the global weak form for the global domain. So, we reduce such problems to a system of algebraic equations. To indicate the efficiency of the present scheme, four examples are discussed in various types of domains and with uniform and nonuniform nodal distribution in 2D cases. Also, to show the validity of the method in this example, a comparison with a valid method has been made. Moreover, in the last example, the accuracy of our scheme in the 3D case is illustrated for the fractional telegraph equation. [ABSTRACT FROM AUTHOR]

This paper attempts to present an iterative‐computational method for solving weakly singular nonlinear Volterra integral equations (WSNVIEs) of the second type based on rationalized Haar wavelets (RHWs). The proposed algorithm does not need to solve any linear or nonlinear system for evaluating the wavelet coefficients. After a brief introduction of rationalized Haar functions (RHFs), the computational matrices of integration and fractional integral are applied to reduce the approximation of integral equations to some matrix algebraic equations. Next, the error analysis of the problem by using the two‐dimensional iterated projection operator is offered. We will prove that the rate of convergence of the proposed algorithm is O(βh), where h is the iteration number and β is the contraction constance. The method for any WSNVIE of the second kind with 0 ≤ β < 1 is convergent. The proposed method is computationally attractive, and comparing the results obtained of the known technique is more efficient. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the solutions of a class of ψ-Hilfer fractional differential equations with the initial values in the sense of -fractional integral by using the successive approximation techniques. Next, the continuous dependence of a solution for the given Cauchy-type problem is presented. [ABSTRACT FROM AUTHOR]