Results 41 to 50 of about 20,315 (242)

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

On Conformable, Riemann-Liouville, and Caputo fractional derivatives

Bulletin of Applied Mathematics and Mathematics Education, 2022
This article compares conformable fractional Derivative with Riemann-Liouville and Caputo fractional derivative by comparing solutions to fractional ordinary differential equations involving the three fractional derivatives via the numerical simulations of the solutions.
Bambang Hendriya Guswanto, Leony Rhesmafiski Andini, Triyani Triyani   +2 more
openaire   +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

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

Numerical approximation of Riemann‐Liouville definition of fractional derivative: From Riemann‐Liouville to Atangana‐Baleanu

Numerical Methods for Partial Differential Equations, 2018
In the last decade, theoretical and applied studies were done in order to provide a suitable definition of fractional derivative, which meets all the requirement of a derivative in its primary sense. It was concluded by some eminent researchers that the Riemann‐Liouville version was the most suitable. However, many numerical approximation of fractional
A. Atangana, J. F. Gómez‐Aguilar
semanticscholar   +3 more sources

Integral-Type Fractional Equations with a Proportional Riemann–Liouville Derivative [PDF]

Journal of Mathematics, 2021
In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution. Also, we give an example to illustrate our work.
openaire   +2 more sources

Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives

AIMS Mathematics, 2019
The fractional input stability of the electrical circuit equations described by the fractional derivative operators has been investigated. The Riemann-Liouville and the Caputo fractional derivative operators have been used.
Ndolane Sene
doaj   +1 more source

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

The unified Riemann-Liouville fractional derivative formulae

Tamkang Journal of Mathematics, 2005
In this paper, we obtain two unified fractional derivative formulae. The first involves the product of two general class of polynomials and the multivariable $H$-function. The second fractional derivative formula also involves the product of two general class of polynomials and the multivariable $H$-function and has been obtained by the application of ...
Soni, R. C., Singh, Deepika
openaire   +3 more sources