Results 51 to 60 of about 20,315 (242)

Nabla Fractional Derivative and Fractional Integral on Time Scales

Axioms, 2021
In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann–Liouville sense. We also introduce the nabla fractional derivative in Grünwald–Letnikov sense.
Bikash Gogoi, Utpal Kumar Saha, Bipan Hazarika, Delfim F. M. Torres, Hijaz Ahmad   +4 more
doaj   +1 more source

Generalized Fractional Nonlinear Birth Processes [PDF]

, 2015
We consider here generalized fractional versions of the difference-differential equation governing the classical nonlinear birth process. Orsingher and Polito (Bernoulli 16(3):858-881, 2010) defined a fractional birth process by replacing, in its ...
BEGHIN, Luisa, Davood Rostamy, Mohsen Alipour   +2 more
core   +1 more source

Solutions to a class of nonlinear differential equations of fractional order [PDF]

, 2009
In this paper we investigate the formulation of a class of boundary value problems of fractional order with the Riemann-Liouville fractional derivative and integral-type boundary conditions.
Kosmatov, Nickolai
core   +1 more source

Fractional variational iteration method via modified Riemann–Liouville derivative

Journal of King Saud University - Science, 2011
AbstractThe aim of this paper is to present an efficient and reliable treatment of the variational iteration method (VIM) for partial differential equations with fractional time derivative. The fractional derivative is described in the Jumarie sense. The obtained results are in good agreement with the existing ones in open literature and it is shown ...
Faraz N., Khan Y., Jafari H., Yildirim A., Madani M.   +4 more
openaire   +2 more sources

Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

Advances in Mathematical Physics, 2013
We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the ...
Mohsen Alipour, Dumitru Baleanu
doaj   +1 more source

Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy

, 2010
With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations.
Adda, Adda, Adda, Agrawal, Agrawal, Almeida, Baleanu, Baleanu, Carpinter, Carpinteri, Carpinteri, Carpinteri, Chen, Chen, Chen, Chen, Cottrill-Shepherd, Cottrill-Shepherd, Cresson, Cresson, El Naschie, El Naschie, El-Nabulsi, El-Nabulsi, El-Nabulsi, Frederico, Fujioka, Fujioka, Guo, Guo-cheng Wu, Jumarie, Jumarie, Jumarie, Jumarie, Kazbekov, Kilbas, Kiryakova, Kolwankar, Kolwankar, Kolwankar, Lakshmikantham, Liang, Ma, Ma, Ma, Malinowska, Miller, Nicholas, Nottale, Nottale, Parvate, Podlubny, Purkait, Riewe, Riewe, Sheng Zhang, Tarasov, Tarasov, Tu, West, Wu, Wu, Wu, Wu, Xia   +64 more
core   +1 more source

A note on fractional Sumudu transform [PDF]

, 2010
We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional ...
Gupta, Vineeta G., Kilicman, Adem, Shrama, Bhavna   +2 more
core   +2 more sources

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