# fractional order

## On the maximal output set of fractional-order discrete-time linear systems

In this paper, we consider a linear discrete-time fractional-order system defined by $\Delta ^{\alpha }x_ {k+1}=Ax_k+B u_k, \quad k \geq 0, \quad x_{0} \in \mathbb{R}^{n};$ $y_{k}=Cx_k, \quad k \geq 0,$ where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $\alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control.  By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, \$\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_

## Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order

This paper proposes the Caputo Fractional Reduced Differential Transform Method (CFRDTM) for Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model with fractional order in a host community.  CFRDTM is the combination of the Caputo Fractional Derivative (CFD) and the well-known Reduced Differential Transform Method (RDTM).  CFRDTM demonstrates feasible progress and efficiency of operation.  The properties of the model were analyzed and investigated.  The fractional SEIR epidemic model has been solved via CFRDTM successfully.  Hence, CFRDTM provides the solutions of the model in the fo

## Robust Stability of Fractional Electromechanical Systems

The engineering methodology for determining robust stability for electromechanical systems (EMS), described by fractional order models, has been developed in this paper. Dynamic EMS described by transfer functions with fractional characteristic polynomial with three terms, have been investigated. The stability of such systems has been analysed by means of applying Riemann complex plane.