In the 1960s Mandelbrot introduced the concept of fractals. Fractals show self-similar structures that their main property is non-integer Hausdorff dimension. Fractality can exist either in space or in time. Fractals have many applications in various branches of science and engineering.

Nowadays, it is known that there is a close connection between fractals and fractional dynamics.

Fractional dynamics is tied to the underlying fractal topology of space-time and studies the behavior of nonlinear physical systems that are characterized by power-law long-range spatial correlations or long-term memory and fractal or multi-fractal properties and described by differential and integral operators of non-integer orders. During the last years, the number of applications of fractional dynamics in science and particularly in physics has been steadily growing and includes models of fractional relaxation and oscillation phenomena, anomalous transport in fluids and plasma, wave propagation in complex media, viscoelastic materials, non-Markovian evolution of quantum fields, networks of fractional oscillators and so on.

In this special issue we will deal with the relationship between the fractality and fractional dynamics and their applications. Potential subjects of this special issue include:
1. Fractional calculus of fractal functions.
2. Applications of fractional models in description of fractal distributions.
3. Applications of fractional calculus and fractal operators in sciences and engineering such as physics and biophysics, mechanics.
4. Modeling of electrical, mechanical, thermal , economical and financial systems using fractional and fractal operators