Scaling (power-type) laws and self-similarity reveal the fundamental property of some “pathological” mathematical objects such as nondifferentiable functions and fractals, which is an expedient method to investigate data. A self-similar (scaling) object repeats itself at different scales in space or time. The property of self-similarity gives us a better opportunity to study phenomena from all analytical and computational aspects.

Scale dependence and multiscale analysis are peculiar properties of some families of special functions and can be observed in nature. A continuous scale transformation from one scale to another implies a generalization and suitable extension of differential operator, as it happens with fractional derivatives.

Dynamical processes and systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science. From the analytical point of view, these kinds of problems often lead us to deal with the concepts of scales, fractals, and fractional operators. For instance, medical images nowadays play an essential role in detection and diagnosis of numerous diseases, and a suitable scale-depending interpretation of the images is a fundamental aspect of the clinical investigation. Nonlinear analysis of data collected by modern devices offers still unsolved analytical problems related to complex physics, abstract mathematical theories, and nonlinear science.

The focus of this special issue is both on the abstract mathematical models on scaling and self-similarity and on the applied computations on those dynamical processes and systems of fractional order towards the applications in all aspects of theoretical and practical study in analysis.

We are soliciting original high quality research papers on topics of interest connected with scaling and self-similarity. Potential topics include, but are not limited to:

• Self-similar analytical problems and scale-depending theoretical and applied analytical problems
• Fractals, nondifferentiable functions, and theoretical and applied analytical problems of fractal type
• 1/f process, fractional Brownian motion, fractional Gaussian noise, self-similar processes, long memory processes, heavy-tailed random processes, and power-law systems
• Fractional differential/integral equations, fractional operators, and systems of fractional order
• Complex systems and nonlinear processing
• Wavelets
• Scaling and self-similarity in applications by focusing on theoretical and analytical aspects arising, e.g., in nonlinear analysis of data, image analysis, data science, and system science

Before submission authors should carefully read over the journal’s Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/aaa/ssss/ according to the following timetable: