Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives

Abstract

The fractional input stability of the electrical circuit equations described by the fractional derivative operators has been investigated. The Riemann-Liouville and the Caputo fractional derivative operators have been used. The analytical solutions of the electrical circuit equations have been developed. The Laplace transforms of the Riemann-Liouville, and the Caputo fractional derivative operators have been used. The graphical representations of the analytical solutions of the electrical circuit equations have been presented. The converging-input converging-state property of the electrical RL, RC and LC circuit equations described by the Caputo fractional derivative, and the global asymptotic stability property of the unforced electrical circuit equations have been illustrated.