LEADER 03042nam 2200565 450 001 9910814343203321 005 20230809233509.0 010 $a3-11-053427-4 010 $a3-11-053513-0 024 7 $a10.1515/9783110535136 035 $a(CKB)4210000000001277 035 $a(MiAaPQ)EBC5049533 035 $a(DE-B1597)477871 035 $a(OCoLC)1004563253 035 $a(OCoLC)1004878517 035 $a(DE-B1597)9783110535136 035 $a(Au-PeEL)EBL5049533 035 $a(CaPaEBR)ebr11443178 035 $a(CaONFJC)MIL1036858 035 $a(EXLCZ)994210000000001277 100 $a20171016h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aNature's patterns and the fractional calculus /$fBruce J. West 210 1$aLeiden, Netherlands ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (200 pages) $cillustrations 225 0 $aFractional Calculus in Applied Sciences and Engineering,$x2509-7210 ;$vVolume 2 311 $a3-11-053411-8 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tForeword -- $tAcknowledgement -- $tContents -- $t1. Complexity -- $t2. Empirical allometry -- $t3. Statistics, scaling and simulation -- $t4. Allometry theories -- $t5. Strange kinetics -- $t6. Fractional probability calculus -- $tEpilogue -- $tBibliography -- $tIndex 330 $aComplexity 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 606 $aFractional calculus 606 $aFractional differential equations 606 $aMathematical models 615 0$aFractional calculus. 615 0$aFractional differential equations. 615 0$aMathematical models. 676 $a515.83 700 $aWest$b Bruce J.$048667 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814343203321 996 $aNature's patterns and the fractional calculus$94126064 997 $aUNINA