Results 51 to 60 of about 611,053 (243)

On a New Class of Fractional Calculus of Variations and Related Fractional Differential Equations [PDF]

arXiv, 2021
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on the classical notion of fractional derivatives, the fractional calculus of variations considered in this paper is ...
arxiv  

FRACTAL RADIOPHYSICS. Part 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS [PDF]

Radio Physics and Radio Astronomy
Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics.
O. V. Lazorenko, L. F. Chernogor
doaj   +1 more source

Concavity in fractional calculus

Filomat, 2018
We discuss a concavity like property for functions u satisfying D?0+u ? C[0, b] with u(0) = 0 and -D?0+u(t) ? 0 for all t ? [0,b]. We develop the property for ? ? (1,2], where D?0+ is the standard Riemann-Liouville fractional derivative. We observe the property is also valid in the case ? = 1. Finally, we show that under certain conditions,
Eloe, Paul W., Neugebauer, Jeffrey T.
openaire   +2 more sources

Applications of Fractional Calculus to Newtonian Mechanics [PDF]

, 2017
We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a constant force ...
Varieschi, Gabriele U.
core   +3 more sources

The memory effect on fractional calculus: an application in the spread of COVID-19

Computational and Applied Mathematics, 2020
Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type ...
L. C. Barros, M. Lopes, F. S. Pedro, E. Esmi, J. P. C. D. Santos, D. Sánchez   +5 more
semanticscholar   +1 more source

Fractional Vector Calculus and Fractional Maxwell's Equations

, 2011
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the
Belleguie, Ben Adda, Ben Adda, Ben Adda, Ben Adda, Brandt, Chen, Cottrill-Shepherd, Engheta, Foley, Gelfand, Genchev, Hussain, Hussain, Kazbekov, Kilbas, Kiryakova, Laskin, Mashhoon, Mashhoon, Mashhoon, McBride, Meerschaert, Metzler, Metzler, Miller, Montroll, Naqvi, Naqvi, Nishimoto, Oldham, Pierantozzi, Podlubny, Ross, Rubin, Samko, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Tarasov, Vasily E. Tarasov, West, Zaslavsky, Zaslavsky   +55 more
core   +1 more source

A finite element method for time fractional partial differential equations [PDF]

, 2011
This is the authors' PDF version of an article published in Fractional calculus and applied analysis© 2011. The original publication is available at www.springerlink.comThis article considers the finite element method for time fractional differential ...
Ford, Neville J., Xiao, Jingyu, Yan, Yubin   +2 more
core   +1 more source

Marvels of fractional calculus

Tbilisi Mathematical Journal, 2017
This is an expository article that describes, in brief, one of the preeminent branch of applicable mathematics, roots of which lie in the nucleus of pure mathematics that ruled the research since past six decades. In writing this article though several important research papers were excised yet attempt is made to retain the beauty of fractional ...
Banerji, P. K., Loonker, Deshna
openaire   +3 more sources

Implementation of fractional order integrator/differentiator on field programmable gate array

Alexandria Engineering Journal, 2016
Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus ...
K.P.S. Rana, V. Kumar, N. Mittra, N. Pramanik   +3 more
doaj   +1 more source

A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String [PDF]

, 2010
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional versions of the
Almeida, Ricardo, Malinowska, Agnieszka B., Torres, Delfim F. M.   +2 more
core   +4 more sources