First order Plus Fractional Diffusive Delay Modeling: Interconnected Discrete Systems

This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty the FOPFDD is (FDD) term, an exponential non-integer order $\alpha$, i.e. $e^{-(Ls)^{\alpha}}$ in Laplace domain. special cases $\alpha = 0.5$ and 1$ have already been investigated thoroughly. In this work $\alpha$ generalized to any real number interval $]0,1[$. For $\alpha=0.5$, term appears solution distributed diffusion systems, which will serve as source inspiration for work. Both frequency time domain are investigated. However, regarding latter, no closed-form expression inverse transform FDD can be found all so numerical tools used obtain impulse response FDD. To establish algorithm, several properties proven: firstly, existence secondly, invariance integral response, thirdly, dependency response's energy on $\alpha$. conclude, model fitted delay-dominant, diffusive-like resistors-capacitors (RC) circuits show increased accuracy compared other state-of-the-art models literature. outperforms approximation accurately tracking functions well mimicing peculiar delay/diffusive-like responses, coming from interconnection large discrete subsystems. fractional character makes it ideal candidate approximate these complex only few parameters.