04620nam 2201045z- 450 991056646810332120220506(CKB)5680000000037699(oapen)https://directory.doabooks.org/handle/20.500.12854/81009(oapen)doab81009(EXLCZ)99568000000003769920202205d2022 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierFractional Calculus and the Future of ScienceBaselMDPI - Multidisciplinary Digital Publishing Institute20221 online resource (312 p.)3-0365-2826-1 3-0365-2827-X Newton 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.Mathematics and SciencebicsscResearch and information: generalbicsscbig datachaoscomplex systemscomplexitycontinuous time random walkcontinuous time random walkscontrol theorydiffusion-wave equationdistributed-order operatorsdiversityDow Jonesentropyfalse positive ratefinancial indicesfractalsfractional calculusfractional conservations lawsfractional diffusionfractional dynamicsfractional order PID controlfractional PINNfractional Poisson process complex systemsfractional relaxationfractional telegrapher's equationfractional-order thinkingfrequency-domain control designGaussian watermarksheavytailednessLaplace and Fourier transformLévy measureliouville-caputo fractional derivativelocal discontinuous Galerkin methodslogistic differential equationmachine learningMittag-Leffler functionsmultidimensional scalingn/aoptimal tuningphysics-informed learningPMSMPoisson process of order kreaction kineticsreaction-diffusion equationsrunning averagesemi-fragile watermarking systemSkellam processstability estimatestatistical assessmentsubordinationtelegrapher's equationstransport problemstransport processesturbulent flowsvariabilityvariable fractional modelviscoelasticityWright functionsMathematics and ScienceResearch and information: generalWest Bruce Jedt48667West Bruce JothBOOK9910566468103321Fractional Calculus and the Future of Science3038653UNINA