Results 31 to 40 of about 52,407 (243)

A new Riemann–Liouville type fractional derivative operator and its application in generating functions

Advances in Difference Equations, 2018
Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and ...
M. Shadab, M. Faisal Khan, J. Luis Lopez-Bonilla   +2 more
doaj   +1 more source

The Nehari manifold for a boundary value problem involving Riemann–Liouville fractional derivative

Advances in Differential Equations, 2018
We aim to investigate the following nonlinear boundary value problems of fractional differential equations: (Pλ){−tD1α(|0Dtα(u(t))|p−20Dtαu(t))=f(t,u(t))+λg(t)|u(t)|q−2u(t)(t∈(0,1)),u(0)=u(1)=0, $$\begin{aligned} (\mathrm{P}_{\lambda}) \left ...
K. Saoudi, P. Agarwal, Poom Kumam, A. Ghanmi, P. Thounthong   +4 more
semanticscholar   +1 more source

A Survey on Semilinear Differential Equations and Inclusions Involving Riemann-Liouville Fractional Derivative

, 2009
We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative.
R. Agarwal, M. Belmekki, M. Benchohra
semanticscholar   +1 more source

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 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

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

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

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

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