Fractional Calculus and the Future of Science

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

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 scientifi...