Results 1 to 10 of about 56,789 (179)

Fractional Ito calculus

Transactions of the American Mathematical Society, Series B
We derive Itô–type change of variable formulas for smooth functionals of irregular paths with nonzero p p th variation along a sequence of partitions, where p ≥ 1 p \geq 1 is arbitrary, in terms of fractional derivative operators.
Cont, R, Jin, R
openaire   +2 more sources

Fractional Calculus and Shannon Wavelet [PDF]

Mathematical Problems in Engineering, 2012
An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any L2(ℝ) function, reconstructed by Shannon wavelets, we can easily define its fractional derivative.
openaire   +3 more sources

Joining Spacetimes on Fractal Hypersurfaces

, 2018
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in understanding ...
Anand, Ankit, Chatterjee, Ayan
core   +1 more source

Application of Fractional Calculus in Engineering [PDF]

, 2011
Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. It has been recognized the advantageous use of this mathematical tool in the modelling and control of many dynamical systems.
Machado, J. A. Tenreiro, Jesus, Isabel S., Barbosa, Ramiro S., Silva, Manuel F., Reis, Cecília   +4 more
openaire   +4 more sources

A survey on fractional variational calculus [PDF]

, 2019
This is a preprint of a paper whose final and definite form is in 'Handbook of Fractional Calculus with Applications. Vol 1: Basic Theory', De Gruyter.
Almeida, Ricardo, Torres, Delfim F. M.
openaire   +3 more sources

Fractional Calculus in Wave Propagation Problems [PDF]

, 2012
Fractional calculus, in allowing integrals and derivatives of any positive order (the term "fractional" kept only for historical reasons), can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where ...
Mainardi, Francesco
core  

Diffusion on middle-$\xi$ Cantor sets

, 2018
In this paper, we study $C^{\zeta}$-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions.
Baleanu, Dumitru, Fernandez, Arran, Golmankhaneh, Ali Khalili, Golmankhaneh, Alireza Khalili   +3 more
core   +1 more source

Operators of Fractional Calculus and Their Applications [PDF]

Mathematics, 2018
n ...
openaire   +5 more sources

Holder exponents of irregular signals and local fractional derivatives

, 1997
It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations.
A Arneodo, A B Chhabra, A Juneja, A Ott, A S Besicovitch, A Zygmund, Anil D Gangal, B B Mandelbrot, B B Mandelbrot, B B Mandelbrot, B Ross, C Meneveau, E M Stein, E M Stein, G H Hardy, G H Hardy, G Jumarie, G M Zaslavsky, G V Welland, H C Fogedby, H E Roman, I Daubechies, I Eyink, J D Farmer, J F Muzy, J Feder, J Gerver, J J Duistermaat, J L Kaplan, J P Bouchaud, K B Oldham, K Falconer, K L Sebastian, K M Kolwankar, K S Miller, K Sarkar, Kiran M Kolwankar, L F Abott, M F Schlesinger, M F Shlesinger, M F Shlesinger, M F Shlesinger, M Giona, M H Jensen, M Holschneider, M Holschneider, M V Berry, M Zähle, N Patzschke, P Collet, P Constantin, P Constantin, R Benzi, R Benzi, R Cawley, R D Mauldin, R Hilfer, R Hilfer, R P Feynmann, R Riedi, S Jaffard, T C Halsey, T H Solomon, T J Osler, T Vicsek, T W Körner, U Frisch, W G Glöckle, W R Schneider, W Wyss   +69 more
core   +2 more sources

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

, 2006
Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived.
Caputo M, Carpinteri A, Cottrill-Shepherd K, Dubrovin B A, Fillipov V M, Goldstein H, Griffiths P A, Helmholtz H, Hilfer R, Korabel N, Laskin N Zaslavsky G M, Levine R D, Montroll E W, Nicolis G, Nigmatullin R R, Oldham K B, Podlubny I, Sagdeev R Z, Samko S G, Sedov L I, Sedov L I, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Tarasov V E, Vasily E Tarasov, Weitzner H, Zaslavsky G M   +33 more
core   +1 more source