EAN: 9783110534115

NATURES PATTERNS AND THE FRACTIONAL CALCULUS - ...

Complexity increases with increasing system size in everything from organisms to organizations.
The nonlinear dependence of a system's functionality on its size  by means of an allometry
relation  is argued to be a consequence of their joint dependency on complexity (information).
In turn  complexity is proven to be the source of allometry and to provide a new kind of force
entailed by a system's information gradient. Based on first principles  the scaling behavior of
the probability density function is determined by the exact solution to a set of fractional
differential equations. The resulting lowest order moments in system size and functionality
gives rise to the empirical allometry relations. Taking examples from various topics in nature
the book is of interest to researchers in applied mathematics  as well as  investigators in the
natural  social  physical and life sciences. ContentsComplexityEmpirical allometryStatistics 
scaling and simulationAllometry theoriesStrange kineticsFractional probability calculus

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