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Degenerate Linear Evolution Equations with the Riemann–Liouville Fractional Derivative

Siberian Mathematical Journal, 2018
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V. Fedorov, M. Plekhanova, R. R. Nazhimov   +2 more
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Fractional Ince equation with a Riemann-Liouville fractional derivative

Applied Mathematics and Computation, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Parra-Hinojosa, J. Gutiérrez-Vega
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Numerical approximation of Riemann‐Liouville definition of fractional derivative: From Riemann‐Liouville to Atangana‐Baleanu

Numerical Methods for Partial Differential Equations, 2017
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
Abdon Atangana, J. F. Gómez‐Aguilar
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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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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.
Jean-Claude Trigeassou, Nezha Maamri, Alain Oustaloup   +2 more
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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
Trifce Sandev, Ralf Metzler, Živorad Tomovski   +2 more
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Approximate Controllability of Fractional Evolution Systems with Riemann--Liouville Fractional Derivatives

SIAM Journal on Control and Optimization, 2015
Summary: 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.
Liu, Zhenhai, Li, Xiuwen
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On a backward problem for fractional diffusion equation with Riemann‐Liouville derivative

Mathematical Methods in the Applied Sciences, 2019
In the present paper, we study the initial inverse problem (backward problem) for a two‐dimensional fractional differential equation with Riemann‐Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well‐posed in the sense of Hadamard. A truncated method is used to construct an approximate
Nguyen Huy Tuan, Nguyen Hoang Tuan, Dumitru Baleanu, Tran Ngoc Thach   +3 more
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Analysis of Neutral Stochastic Fractional Differential Equations Involving Riemann–Liouville Fractional Derivative with Retarded and Advanced Arguments

Qualitative Theory of Dynamical Systems, 2023
Shahid Saifullah, Sumbel Shahid, A. Zada
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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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