Esta web utiliza cookies propias y de terceros que nos permiten optimizar tu experiencia en el sitio web, evaluar su rendimiento, generar estadísticas de uso y mejorar y añadir nuevas funcionalidades. Mediante el análisis de tus hábitos de navegación podemos mostrar contenidos más relevantes y medir las interacciones con la web.
Puede obtener más información aquí.

Avanzado
Artículos
Portada

FRACTIONAL CALCULUS AND THE FUTURE OF SCIENCE IBD

BRUCE J WEST
MDPI AG
04 / 2022
9783036528267
Inglés

Sinopsis

Newton foresaw the limitations of geometryâÇÖs 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.áTwo 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 NewtonâÇÖs laws. MandelbrotâÇÖs mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the NewtonâÇÖs 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 NewtonâÇÖs laws to describe the many guises of complexity, most of which lay beyond NewtonâÇÖs experience, and many had even eluded MandelbrotâÇÖs powerful intuition. The bookâÇÖs authors look behind the mathematics and examine what must be true about a phenomenonâÇÖs 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.