03042nam 2200565 450 991081434320332120230809233509.03-11-053427-43-11-053513-010.1515/9783110535136(CKB)4210000000001277(MiAaPQ)EBC5049533(DE-B1597)477871(OCoLC)1004563253(OCoLC)1004878517(DE-B1597)9783110535136(Au-PeEL)EBL5049533(CaPaEBR)ebr11443178(CaONFJC)MIL1036858(EXLCZ)99421000000000127720171016h20172017 uy 0engurcnu||||||||rdacontentrdamediardacarrierNature's patterns and the fractional calculus /Bruce J. WestLeiden, Netherlands ;Boston, [Massachusetts] :De Gruyter,2017.©20171 online resource (200 pages) illustrationsFractional Calculus in Applied Sciences and Engineering,2509-7210 ;Volume 23-11-053411-8 Includes bibliographical references and index.Frontmatter -- Foreword -- Acknowledgement -- Contents -- 1. Complexity -- 2. Empirical allometry -- 3. Statistics, scaling and simulation -- 4. Allometry theories -- 5. Strange kinetics -- 6. Fractional probability calculus -- Epilogue -- Bibliography -- IndexComplexity 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 Fractional calculusFractional differential equationsMathematical modelsFractional calculus.Fractional differential equations.Mathematical models.515.83West Bruce J.48667MiAaPQMiAaPQMiAaPQBOOK9910814343203321Nature's patterns and the fractional calculus4126064UNINA