Energy harvesting using piezoelectric materials is nowadays an efficient way for powering low-power electronic devices. Supplying the energy of wireless sensors, used in condition and health monitoring of bridges and other civil structures, is one of the applications of the energy harvester systems. The main issue in the linear energy harvesting systems is that their best performance is limited to the narrow band around the resonance frequency. To overcome this issue a nonlinear energy harvester is presented in this study. Researchers present that getting exposed to the alternating mechanical stress over a long time will result in the decay of charge produced by piezoelectric transduction mechanism and this decay will comply with a fractional power law of the time. Governing equations of the Euler-Bernoulli beam with piezoelectric patches under nonlinear magnetic force and base excitation have been extracted. The damping of this system is assumed to be fractional damping. The mode shapes of the beam with two different cross sections are derived and by using the assumed mode method the first mode is used to derive an approximate result of the electromechanical system. Analytical results in the linear and nonlinear system with parallel and series connections are validated by experimental results. The accuracy of the model is shown by comparing the numerical and experimental results. After calculating the optimum electrical resistance by experimental and analytical approaches the output power of the provided harvester under different factors like fractional order, excitation frequency and base excitation and electrical resistance for the integer and fractional damping has been discussed by the voltage-time, bifurcation, Poincare and phase diagrams in the MATLAB environment Keywords: Energy harvesting, Piezoelectric, Fractional damping, Nonlinear magnetic force