Volterra's integral equations with local and nonlocal loads represent the novel class of integral equations that have attracted considerable attention in recent years. These equations are a generalisation of the classic Volterra integral equations, which were first introduced by Vito Volterra in the late 19th century. The loaded Volterra integral equations are characterised by the presence of a load which complicates the process of their theoretical and numerical study. Sometimes these equation are called the equations with ``frozen'' argument. The present work is devoted to the study of Volterra equations with locally loaded integral operators. The existence and uniquness theorems are proved. Among the main contributions is the collocation method for approximate solution of such equations based on the piecewise linear approximation. To confirm the convergence of the method, a number of numerical results for solving model problems are provided.

翻译：局部与非局部加载的Volterra积分方程是近年来备受关注的新型积分方程类别。这类方程是经典Volterra积分方程的推广，后者由Vito Volterra于19世纪末首次提出。加载型Volterra积分方程的特征在于存在加载项，这使其理论与数值研究过程变得复杂。这类方程有时也被称为具有"冻结"自变量的方程。本研究致力于探讨具有局部加载积分算子的Volterra方程，证明了其解的存在唯一性定理。主要贡献之一是建立了基于分段线性近似的配置法来求取此类方程的近似解。为验证方法的收敛性，文中给出了求解模型问题的若干数值结果。