An overview of some recent published and unpublished results on positive fractional continuous-time and discrete-time linear systems is given. The first part of the paper is devoted to the positive continuous-time fractional systems. For those systems the solutions to the fractional state equations are proposed. Necessary and sufficient conditions for the positivity, reachability and stability ...

There exists a great number of work related to chaotic systems investigated by many researchers, especially about Lorenz chaotic system. If the order of differentiation of variables are fractional, the systems are called fractional chaotic systems. In this work a webbased interface is designed for fractional composition of five different chaotic systems. The interface takes initial and fraction...

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear behavior can be found in engineering, management science, econ...

The main aim of this contribution is to introduce the fundamentals of the Fractional Order Calculus (FOC) and outline its possible application to analysis and synthesis of control systems. The basic theoretical concepts of FOC are followed by techniques for potential fractional order systems description and stability investigation. Moreover, the paper offers the overview of the existing fractio...

This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapu...