Results 41 to 50 of about 52,407 (243)

Fractional generalizations of filtering problems and their associated fractional Zakai equations [PDF]

, 2014
In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering
Daum, Frederick, Nelson, Kenric, Umarov, Sabir   +2 more
core   +1 more source

Analysis and Modeling of Fractional-Order Buck Converter Based on Riemann-Liouville Derivative

IEEE Access, 2019
In previous studies, researchers used the fractional definition of Caputo to study fractional-order power converter. However, it is found that the model based on Caputo fractional definition is inconsistent with the actual situation.
Zhihao Wei, Bo Zhang, Yanwei Jiang
doaj   +1 more source

Weyl Quantization of Fractional Derivatives

, 2009
The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives.
Kilbas A. A., Miller K., Oldham K. B., Podlubny I., Samko S. G., Tarasov V. E., Vasily E. Tarasov, Yosida K., Zaslavsky G. M.   +8 more
core   +1 more source

Gauge invariance in fractional field theories [PDF]

, 2008
The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$.
Abers, Baleanu, Baleanu, Caputo, Chiu, Edmonds, Feller, Goldfain, Grünwald, Herrmann, Herrmann, Lim, Liouville, Miller, Oldham, Pauli, Podlubny, Raspini, Raspini, Richard Herrmann, Riemann, Riesz, Sakurai, Weyl, Wilson, Yang, Yao, Zavada, Zeeman   +28 more
core   +1 more source

Fourth-order effective approximation of the normalized Riemann-Liouville tempered fractional derivatives and its applications

AIMS Mathematics
In this paper, a fourth-order quasi-compact approximation for the normalized Riemann-Liouville tempered fractional derivatives was proposed. Its effectiveness was proved by using the generating function method, and it was applied to the numerical ...
Jianxin Li, Zeshan Qiu
doaj   +1 more source

Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

Abstract and Applied Analysis, 2014
By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under ...
Wenzhe Xie, Jing Xiao, Zhiguo Luo
doaj   +1 more source

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Results in Physics, 2016
In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI) equation with Riemann–Liouville derivative is performed.
Emrullah Yaşar, Yakup Yıldırım, Chaudry Masood Khalique   +2 more
doaj   +1 more source

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative [PDF]

, 2007
2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones.
Luchko, Yury, Trujillo, Juan
core  

On the Leibniz rule and Laplace transform for fractional derivatives

, 2019
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly.
Liu, Da-Yan, Tse, Peter W., Wang, Yong, Wei, Yiheng   +3 more
core   +3 more sources

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics, 2020
This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem.
Idris Ahmed, Poom Kumam, K. Shah, Piyachat Borisut, K. Sitthithakerngkiet, Musa A. Demba   +5 more
semanticscholar   +1 more source