Results 221 to 230 of about 9,528 (243)

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
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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
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Riemann-Liouville Fractional Derivative and Application to Model Chaotic Differential Equations

, 2018
In this work, the stability analysis and numerical treatmen t of chaotic time-fractional differential equations are co nsidered. The classical system of ordinary differential equations wi th initial conditions is generalized by replacing the firstorder ...
K. M. Owolabi
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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
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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
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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.
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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
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Approximate controllability and existence of mild solutions for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2

Fractional Calculus and Applied Analysis, 2019
In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution equations with nonlocal conditions of order 1 < α < 2.
Linxin Shu, X. Shu, J. Mao
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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
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Approximate Controllability of Fractional Evolution Systems with Riemann--Liouville Fractional Derivatives

SIAM Journal on Control and Optimization, 2015
In this paper, we deal with the control systems governed by fractional evolution differential equations involving Riemann--Liouville fractional derivatives in Banach spaces. Our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions.
Xiuwen Li, Zhenhai Liu
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