Abstract
We emphasize at the outset that this is not a traditional text book. The authors do not think that modeling of the complex physical phenomena they have in mind is sufficiently well developed to warrant such a text. On the other hand, this is also not a research monograph, since it lacks the rigor that many would insist on, in such a treatment. So the book falls somewhere in between, resting on a set of lecture notes that have been polished and extended, with the view to providing insight into a new area of investigation in science, particularly in physics. The lectures present techniques from the calculus of fractional derivatives and integrals and fractional stochastic differential equations, but are not intended to form a book about mathematics. Instead of formal mathematics, we emphasize physical interpretation and highlight how to model complex physical phenomena, such as found in the world around us. The use of fractal functions and the applications of fractal operators, such as fractional derivatives and integrals applied to analytic functions, are investigated with a view towards modeling complex physical phenomena. Thus, although the material may appear formal at times, our purpose is to reveal the mechanisms underlying the complexity rather than to obscure them. Therefore we touch lightly on history and philosophy, in addition to physics and mathematics, where we think they can contribute to the discussion.
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West, B.J., Bologna, M., Grigolini, P. (2003). Nondifferentiable Processes. In: Physics of Fractal Operators. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21746-8_1
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