The field of numerical methods is witnessing significant developments in tackling complex models, particularly in the areas of nonlinear distributed delay Sobolev models, fractional Laplacian, and partial integro-differential equations. Researchers are proposing innovative numerical approaches that offer improved stability, accuracy, and efficiency. Notably, the use of non-standard bases in Finite Element methods and the development of tailored discretization techniques for non-local integral terms are showing promising results. These advancements have the potential to impact various applications, including option pricing and power plant management. Noteworthy papers include: The paper on Finite Elements with weighted bases for the fractional Laplacian, which presents a novel approach achieving higher convergence rates. The paper on Numerical methods for solving PIDEs arising in swing option pricing, which proposes second-order numerical methods for convection-dominated equations with nonlocal integral terms.