Clinical Applications of Fractals and Fractional Order Systems

Fractional calculus as a generalization of integer-order calculus has been used widely in biology, physics, and finance. The major advantage of fractional-order to integer-order operators is their ability to reveal the complicated dynamics of given systems which makes them a more realistic framework to model different biological and physical phenomena. While the integer-order models provide a small class of non-integer order models, using fractional order operators, we can study different classes of the same model by changing the fractional-order. Therefore, these models provide us more flexibility to analyze and control the behavior of a system. During recent decades many efforts in the area of fractal geometry have been made to discover and control the nonlinear and complicated dynamics of different systems that exhibit fractal processes. A fractal has been defined as a subset of Euclidean space with a dimension strictly higher than its topological dimension. For the first time, Mandelbrot in 1983 introduced these irregular geometric objects to the world. Fractals also can be defined as physical models for different phenomena which are distributed evenly in the embedding space. Fractals are well-known because of their unique property which is self-similarity in different scales. During recent decades, researchers in different field of sciences have developed varieties of interesting studies about the unique properties of fractals.