Dear Colleagues,

Three centuries ago, Newton transformed Natural Philosophy into today’s Science by focusing on change and quantification, and he did so in a way that resonated with the scientific community of his day. His arguments appeared to be geometric in character, and nowhere in the Principia do you find explicit reference to fluxions or to differentials. What Newton did was reveal the entailments of the calculus and convince generations of scientists of the value of their focusing on how physical objects change in space and time. Some contemporary mathematicians of his generation recognized what he had done, but their number could be counted on one hand, and their comments are primarily of historical interest only.

Fast-forward to today and Modern Science, from Anatomy to Zoology, is seen to have absorbed the transformational effect of Newton’s contribution to how we quantitatively and qualitatively understand the world, the fundamental importance of motion. However, it has occurred to a number of the more philosophically attuned contemporary scientists that we are now at another point of transition, where the implications of complexity, memory, and uncertainty have revealed themselves to be barriers to our future understanding of our technological society. Fractional calculus (FC) has emerged from the shadows as a way of taming the three horsemen in the figure with a methodology capable of analytically outdistancing these imposters.

We are looking for imaginative articles that implement FC and reveal its transformational nature, including but not limited to such things as: how a fractional derivative in time incorporates memory into the solution of the dynamic description of an earthquake, a brain quake or a crash in the stock market; how the fractional derivative in space incorporates spatial nonlocality into the solution of the complex dynamical descriptions of a riot, the collective intelligence of social groups, or the neuronal activity of the brain; or how the combined fractional derivatives in both time and space of measures of uncertainty incorporate both memory and nonlocality into the phase space solution to capture the limited uncertainty of an ensemble of fractal trajectories, or the scaling behavior of complex dynamical networks.

In short, we are seeking submissions in which the authors look behind the mathematics and examine what must be true about the phenomenon in order to justify the replacement of an ordinary derivative with a fractional derivative before they solve the new equations. For example, an insightful and extended explanatory description as to why one ought to expect the flow equations for honey and water to be different followed with a comparison of the solutions to the ordinary and fractional equations with data would constitute a paradigm for a submission. The desired articles are intended to provide the reader with a window into the future of a specific piece of science through the lens of FC and how that lens will make you think differently about that area of science. Thus, a perfect submission will be more about the intellectual implications and utility of the FC than it is about its formal structure in chemistry, epidemiology, sociology, psychology, physics, or any other scientific discipline.  

Prof. Dr. Bruce J. West
Guest Editor

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