LEADER 04593nam 2201021z- 450 001 9910566468103321 005 20231214133427.0 035 $a(CKB)5680000000037699 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/81009 035 $a(EXLCZ)995680000000037699 100 $a20202205d2022 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional Calculus and the Future of Science 210 $aBasel$cMDPI - Multidisciplinary Digital Publishing Institute$d2022 215 $a1 electronic resource (312 p.) 311 $a3-0365-2826-1 311 $a3-0365-2827-X 330 $aNewton foresaw the limitations of geometry?s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton?s laws. Mandelbrot?s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton?s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton?s laws to describe the many guises of complexity, most of which lay beyond Newton?s experience, and many had even eluded Mandelbrot?s powerful intuition. The book?s authors look behind the mathematics and examine what must be true about a phenomenon?s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding. 606 $aResearch & information: general$2bicssc 606 $aMathematics & science$2bicssc 610 $afractional diffusion 610 $acontinuous time random walks 610 $areaction-diffusion equations 610 $areaction kinetics 610 $amultidimensional scaling 610 $afractals 610 $afractional calculus 610 $afinancial indices 610 $aentropy 610 $aDow Jones 610 $acomplex systems 610 $aSkellam process 610 $asubordination 610 $aLe?vy measure 610 $aPoisson process of order k 610 $arunning average 610 $acomplexity 610 $achaos 610 $alogistic differential equation 610 $aliouville-caputo fractional derivative 610 $alocal discontinuous Galerkin methods 610 $astability estimate 610 $aMittag-Leffler functions 610 $aWright functions 610 $afractional relaxation 610 $adiffusion-wave equation 610 $aLaplace and Fourier transform 610 $afractional Poisson process complex systems 610 $adistributed-order operators 610 $aviscoelasticity 610 $atransport processes 610 $acontrol theory 610 $afractional order PID control 610 $aPMSM 610 $afrequency-domain control design 610 $aoptimal tuning 610 $aGaussian watermarks 610 $astatistical assessment 610 $afalse positive rate 610 $asemi-fragile watermarking system 610 $afractional dynamics 610 $afractional-order thinking 610 $aheavytailedness 610 $abig data 610 $amachine learning 610 $avariability 610 $adiversity 610 $atelegrapher's equations 610 $afractional telegrapher's equation 610 $acontinuous time random walk 610 $atransport problems 610 $afractional conservations laws 610 $avariable fractional model 610 $aturbulent flows 610 $afractional PINN 610 $aphysics-informed learning 615 7$aResearch & information: general 615 7$aMathematics & science 700 $aWest$b Bruce J$4edt$048667 702 $aWest$b Bruce J$4oth 906 $aBOOK 912 $a9910566468103321 996 $aFractional Calculus and the Future of Science$93038653 997 $aUNINA