In this paper, the effect of non-zero initial condition on the time domain responses of fractional-order systems using Caputo and Riemann-Liouville (RL) fractional definitions are discussed. Analytical formulas were derived for the step and square wave responses of fractional-order RC? circuit under RL and Caputo operators for non-zero initial condition. Moreover, a simulation scheme for fractional state-space systems with non-zero initial condition is introduced. © 2016 IEEE.
Abdelaty A.M., Radwan A.G., Ahmed W.A., Faied M.
Differentiation (calculus); Analytical formulas; Caputo fractional derivatives; Fractional order; Fractional-order systems; Square-wave response; State space systems; Time domain response; Zero initial conditions; Reconfigurable hardware
2016 13th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, ECTI-CON 2016, Art. No. 7561294, Doi: 10.1109/ECTICon.2016.7561294