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Szász‐Mirakyan operators are a powerful tool that can be used to approximate functions on the unbounded interval [0,∞). In this contribution, we propose a numerical solution of Volterra integral equations with the help of Szász‐Mirakyan operators. In this direction, we provide both numerical scheme and estimation of error bound of solution. Numerical experiments are also presented, highlighting the performance of the new constructions of proposed algorithm in the context of one‐dimensional approximation. [ABSTRACT FROM AUTHOR]

The necessary and sufficient conditions for compactness of a matrix operator between Banach spaces is obtained by utilizing the concept of the Hausdorff measure of noncompactness. This is one of the most interesting application in the theory of sequence spaces. In this paper, the compact operators are characterized on Jordan totient sequence spaces by using the concept of the Hausdorff measure of noncompactness. [ABSTRACT FROM AUTHOR]

This study explores the fractional damped generalized regularized long‐wave equation in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio fractional derivatives. With the aid of fixed‐point theorem in the Atangana‐Baleanu fractional derivative with Mittag‐Leffler–type kernel, we show the existence and uniqueness of the solution to the damped generalized regularized long‐wave equation. The modified Laplace decomposition method (MLDM) defined in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio (in the Riemann sense) operators is used in securing the approximate‐analytical solutions of the nonlinear model. The numerical simulations of the obtained solutions are performed with different suitable values of ρ, which is the order of fractional parameter. We have seen the effect of the various parameters and variables on the displacement in figures. [ABSTRACT FROM AUTHOR]

In this study, approximating the finite Hilbert transform are given for absolutely continuous mappings. Then, some numerical experiments for the obtained approximation are also presented. [ABSTRACT FROM AUTHOR]