Almost-everywhere singular (AES) distributions, usually referred to as multifractal measures, provide an intermediate link between atomic distributions (distributions represented by a countable superposition of Dirac's delta terms) and smooth regular distributions. This article shows how AES distributions can be rigorously treated in connection with distributed-parameter models and presents closed-form expressions and/or recursive, uniformly converging approximation methods for integral transforms (Laplace and Stieltjes). In particular, exact results are obtained and discussed for linear and uniform nonlinear kinetcis and for transport schemes in the presence of continuous mixtures. The physical origin of AES distributions in real systems is also detailed.
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