Results 51 to 60 of about 19,827 (284)

Sturm-Liouville Problem with Mixed Boundary Conditions for a Differential Equation with a Fractional Derivative and Its Application in Viscoelasticity Models

Axioms, 2023
In this study, we obtained a system of eigenfunctions and eigenvalues for the mixed homogeneous Sturm-Liouville problem of a second-order differential equation containing a fractional derivative operator.
Ludmila Kiryanova, Tatiana Matseevich
doaj   +1 more source

Generalized Extended Riemann-Liouville Type Fractional Derivative Operator

Kragujevac Journal of Mathematics, 2023
In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform and integral representations are obtained for these ...
Hafida, Abbas, Abdelhalim, Azzouz, Brahim, Zahaf Mohammed, Mohamed, Belmekki   +3 more
openaire   +2 more sources

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

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

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

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

A multiple Opial type inequality for the Riemann-Liouville fractional derivatives [PDF]

Journal of Mathematical Inequalities, 2013
The aim of this paper is to prove a multiple Opial type inequality for Riemann-Liouville fractional derivatives which is proved for two factors and ordinary derivatives by Fink. Two methods are applied and a comparison of the obtained estimations is also given.
Ivan Perić, Maja Andrić, Josip Pečarić   +2 more
openaire   +1 more source