fractional-order

Domination in linear fractional-order distributed systems

This paper investigates the notion of domination in linear fractional-order distributed systems in a finite-dimensional state.  The objective is to compare or classify the input operators with respect to the output ones, and we present the characterization and property results of this concept.  Then, we examine the relationship between controllability and the notion of domination.  Finally, we provide a numerical example to illustrate our results.

Fractional derivative model for tumor cells and immune system competition

Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing.  So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer's evolution under immunity of the body.  We will analyze the stability of the formulated system at different equilibrium points.  Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer's dynamics.