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Este artículo presenta la deducción matemática de las pérdidas de potencia por conducción en inversores monofásicos de puente H controlados mediante Modulación Senoidal de Ancho de Pulso (SPWM). Se presenta el desarrollo matemático de las ecuaciones de voltaje y corriente a través de los semiconductores durante su estado de conducción y se calcula su disipación de potencia. Las ecuaciones de pérdidas de potencia encontradas dependen de las características de la modulación empleada y de los parámetros de la carga. Mediante validación experimental y de simulaciones se obtuvieron curvas que muestran la validez de las ecuaciones y sus aproximaciones. This paper presents the mathematical derivation of the power losses by conduction in single phase H-bridge inverters controlled by Sinusoidal Pulse Width Modulation (SPWM). The development of the mathematical equations for voltage and current through the semiconductor in its conducting state is presented and the power dissipation is calculated. The power loss equations found depend on the characteristics of the modulation used and on the parameters of the load. Through simulations and experimental validation, curves showing the validity of the equations and their approaches in accordance with the conditions of the test were obtained.

RESUMEN: Trabajo en investigacion sobre solucion de ecuaciones diferenciales de Riemann-Liouville y Caputo. Publicado en revista ELSEVIER. ABSTRACT: In this paper, a numerical method is developed to obtain a solution of Caputo’s and Riemann-Liouville’s Fractional Differential Equations (CFDE and RLFDE). Scientific literature review shows that some numerical methods solve CFDE and there is only one paper that numerically solves RLFDE. Nevertheless, their solution is limited or the Fractional Differential Equation (FDE) to be solved is not in the most general form. To be best of the author’s knowledge, the proposed method is presented as the first method that numerically solves RLFDE which includes multi-order fractional derivatives and variable coefficients. The method converts the RLFDE or CFDE to be solved into an algebraic equation. Each Riemann-Liouville’s or Caputo’s Fractional Derivative (RLFD and CFD), derived from the RLFDE or CFDE respectively, is conveniently written as a set of substitution functions and an integral equation. The algebraic equation, the sets of substitution functions and the integral equations are discretized; and then solved using arrays. Some examples are provided for comparing the obtained numerical results with the results of other papers (when available) and exact solutions. It is demonstrated that the method is accurate and easy to implement, being presented as a powerful tool to solve not only FDE but also a wide range of differential and integral equations.