Fractional Calculus and the Future of Science

• Other Authors: West, Bruce J. (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Research & information: general; Mathematics & science; fractional diffusion; continuous time random walks; reaction-diffusion equations; reaction kinetics; multidimensional scaling; fractals; fractional calculus; financial indices; entropy; Dow Jones; complex systems; Skellam process; subordination; Lévy measure; Poisson process of order k; running average; complexity; chaos; logistic differential equation; liouville-caputo fractional derivative; local discontinuous Galerkin methods; stability estimate; Mittag-Leffler functions; Wright functions; fractional relaxation; diffusion-wave equation; Laplace and Fourier transform; fractional Poisson process complex systems; distributed-order operators; viscoelasticity; transport processes; control theory; fractional order PID control; PMSM; frequency-domain control design; optimal tuning; Gaussian watermarks; statistical assessment; false positive rate; semi-fragile watermarking system; fractional dynamics; fractional-order thinking; heavytailedness; big data; machine learning; variability; diversity; telegrapher's equations; fractional telegrapher's equation; continuous time random walk; transport problems; fractional conservations laws; variable fractional model; turbulent flows; fractional PINN; physics-informed learning; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

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 sci...