Results 81 to 90 of about 611,053 (243)

Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus

Computer Modeling in Engineering & Sciences, 2020
: In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We fi rst give a description to the system by constructing its classical Lagrangian. Secondly, the
D. Baleanu, B. Ghanbari, J. Asad, A. Jajarmi, H. M. Pirouz   +4 more
semanticscholar   +1 more source

On the Rigorous Correspondence Between Operator Fractional Powers and Fractional Derivatives via the Sonine Kernel

Fractal and Fractional
Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address
Zelin Liu, Xiaobin Yu, Yajun Yin
doaj   +1 more source

Fractional Solutions of Bessel Equation with -Method

The Scientific World Journal, 2013
This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques.
Erdal Bas, Resat Yilmazer, Etibar Panakhov   +2 more
doaj   +1 more source

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

On nonlinear fractional Hahn integrodifference equations via nonlocal fractional Hahn integral boundary conditions

AIMS Mathematics
All authors Fractional Hahn differences and fractional Hahn integrals have various applications in fields where discrete fractional calculus plays a significant role, such as in discrete biological modeling and signal processing to handle systems with ...
Nichaphat Patanarapeelert, Jiraporn Reunsumrit, Thanin Sitthiwirattham   +2 more
doaj   +1 more source

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

Discretized fractional substantial calculus [PDF]

ESAIM: Mathematical Modelling and Numerical Analysis, 2014
This paper discusses the properties and the numerical discretizations of the fractional substantial integral $$I_s^ f(x)=\frac{1}{ ( )} \int_{a}^x{\left(x- \right)^{ -1}}e^{- (x- )}{f( )}d , >0, $$ and the fractional substantial derivative $$D_s^ f(x)=D_s^m[I_s^ f(x)], =m- ,$$ where $D_s=\frac{\partial}{\partial x}+ =D+ $, $ $ can ...
Minghua Chen, Weihua Deng
openaire   +2 more sources

Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus

Fractal and Fractional, 2020
Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations.
Arran Fernandez, Iftikhar Husain
doaj   +1 more source

Estimation of generalized fractional integral operators with nonsingular function as a kernel

AIMS Mathematics, 2021
Bessel function has a significant role in fractional calculus having immense applications in physical and theoretical approach. Present work aims to introduce fractional integral operators in which generalized multi-index Bessel function as a kernel, and
Iqra Nayab, Shahid Mubeen, Rana Safdar Ali, Gauhar Rahman, Abdel-Haleem Abdel-Aty, Emad E. Mahmoud, Kottakkaran Sooppy Nisar   +6 more
doaj   +1 more source

Derivatives and integrals: matrix order operators as an extension of the fractional calculus [PDF]

arXiv, 2020
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function applied to the fractional differintegration definition.
arxiv