Results 241 to 250 of about 20,134 (284)

Fractional Langevin equation and Riemann-Liouville fractional derivative

The European Physical Journal E, 2007
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system.
Kwok Sau Fa
semanticscholar   +5 more sources

Fractional Ince equation with a Riemann-Liouville fractional derivative

Applied Mathematics and Computation, 2013
We extend the classical treatment of the Ince equation to include the effect of a fractional derivative term of order @a>0 and amplitude c. A Fourier expansion is used to determine the eigenvalue curves a(@?) in function of the parameter @?, the stability domains, and the periodic stable solutions of the fractional Ince equation.
A. Parra-Hinojosa, J. Gutiérrez-Vega
semanticscholar   +3 more sources

Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications

Fractional Calculus and Applied Analysis, 2021
Mikusiński’s operational calculus is a formalism for understanding integral and derivative operators and solving differential equations, which has been applied to several types of fractional-calculus operators by Y.
Hafiz Muhammad Fahad, A. Fernandez
semanticscholar   +1 more source

The nonlinear Rayleigh‐Stokes problem with Riemann‐Liouville fractional derivative

Mathematical methods in the applied sciences, 2019
The Rayleigh‐Stokes problem has gained much attention with the further study of non‐Newtonain fluids. In this paper, we are interested in discussing the existence of solutions for nonlinear Rayleigh‐Stokes problem for a generalized second grade fluid ...
Yong Zhou, Jing Na Wang
semanticscholar   +1 more source

Initialization of Riemann-Liouville and Caputo Fractional Derivatives

Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B, 2011
Riemann-Liouville and Caputo fractional derivatives are fundamentally related to fractional integration operators. Consequently, the initial conditions of fractional derivatives are the frequency distributed and infinite dimensional state vector of fractional integrators.
Alain Oustaloup, Jean-Claude Trigeassou, Nezha Maamri   +2 more
openaire   +2 more sources

Fractional Approximation by Riemann–Liouville Fractional Derivatives

2020
In this chapter we study quantitatively with rates the pointwise convergence of a sequence of positive sublinear operators to the unit operator over continuous functions. This takes place under low order smoothness, less than one, of the approximated function and it is expressed via the left and right Riemann–Liouville fractional derivatives of it. The
openaire   +2 more sources

Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative

Journal of Physics A: Mathematical and Theoretical, 2011
In this paper, the solution of a fractional diffusion equation with a Hilfer-generalized Riemann–Liouville time fractional derivative is obtained in terms of Mittag–Leffler-type functions and Fox's H-function. The considered equation represents a quite general extension of the classical diffusion (heat conduction) equation. The methods of separation of
Živorad Tomovski, Trifce Sandev, Ralf Metzler, Ralf Metzler   +3 more
openaire   +2 more sources

Diffusive representation of Riemann-Liouville fractional integrals and derivatives

2017 36th Chinese Control Conference (CCC), 2017
This paper presents a novel equivalent description of fractional-order integrals and derivatives via an auxiliary integral function of two variables. Employing the concept of Laguerre integration, a novel approximate scheme for the resulting infinite dimensional state space model is derived.
Baoli Ma, Yuxiang Guo
openaire   +2 more sources

The Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales

2018
In this chapter we suppose that \(\mathbb {T}\) is a time scale with forward jump operator and delta differentiation operator σ and Δ, respectively.
openaire   +2 more sources

Fractional Sobolev space with Riemann–Liouville fractional derivative and application to a fractional concave–convex problem

Advances in Operator Theory, 2021
C. Ledesma, Manuel M. Bonilla
semanticscholar   +1 more source