This paper deals with the solution of a class of Volterra integral equations in the sense of the conformable fractional derivative. For this goal, the well-organized Neumann method is developed and some theorems related to existence, uniqueness, and sufficient condition of convergence are presented. Some illustrative examples are provided to demonstrate the efficiency of the method in solving conformable fractional Volterra integral equations.

We show that a regular von Neumann Q-m-convex Fréchet algebra is of finite dimension. We also show that a regular von Neumann m-convex Fréchet algebra is a projective limit of finite dimensional algebras. Finally, we prove that a bilateral Q-F-algebra is a regular von Neumann algebra if and only if it is isomorphic to a finite product of algebras which are also fields.

A collocation method with the modified equilibrium on line method (ELM) for imposition of Neumann and Robin boundary conditions is presented for solving the two-dimensional acoustical problems. In the modified ELM, the governing equations are integrated over the lines on the Neumann (Robin) boundary instead of the Neumann (Robin) boundary condition equations. In other words, integration domains are straight lines for nodes located on the Neumann boundary. Numerical examples of two-dimensional acoustical problems are presented to demonstrate thestability, accuracy and convergence of the proposed method.

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Let M be a factor von Neumann algebra. It is shown that every nonlinear *-Lie higher derivation D={Æn}nÎN on M is additive. In particular, if M is infinite type I factor, a concrete characterization of D is given.

This research paper investigates the numerical analysis of the damped wave equation (DWE), focusing on the properties of numerical solutions achieved via semi-discrete approximation (SDA) and fully-discrete approximation (FDA) finite element methods (FEMs). This study established the existence of SDA and FDA solutions. Theoretical results are validated with numerical examples conducted in one, two, and three dimensions, demonstrating the accuracy and effectiveness of the proposed approaches.