The paper addresses the application of Volterra integral equations first kind for modeling dynamic power systems. We study problem forecasting commissioning capacities electric system, taking into account various hypotheses about dynamics equipment aging, and known prehistory. numerical results two models to development a large system using example Unified Energy System Russia are presented. Th...

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

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We give asymptotic classification of the positive solutions of a class of two-dimensional nonlinear Volterra integro-differential equations. Also, we furnish necessary and conditions for the existence of such positive solutions.