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Stability analysis of fractional differential system with Riemann–Liouville derivative
Mathematical and Computer Modelling, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Changpin Li +2 more
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The Riemann–Liouville fractional derivative for Ambartsumian equation
Results in Physics, 2020 La ecuación de Ambartsumian, basada en la derivada fraccionaria modificada de Riemann–Liouville, se analiza en este trabajo. La solución se expresa como una serie de potencias de potencias arbitrarias y se ha comprobado su convergencia. Además, mostramos que la presente solución se reduce a los resultados en la literatura cuando la derivada ...
Essam R El-Zahar +2 more
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Complete infinitesimal prolongation of the Riemann–Liouville and Caputo derivatives
Reviews in Mathematical Physics, 2023This paper presents the infinitesimal prolongation to Riemann–Liouville and Caputo fractional derivatives without the restrictive lower limit fixed in the integrals, when applicated to the transformation group. The properties are presented, and the examples are illustrated along with the symmetry to fractional derivative criteria.
Felix S. Costa +4 more
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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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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 equations of Volterra type involving a Riemann–Liouville derivative
Applied Mathematics Letters, 2013 Abstract In this paper, we will discuss the existence of solutions of fractional equations of Volterra type with the Riemann–Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
Tadeusz Jankowski
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Fractional Langevin equation and Riemann-Liouville fractional derivative
The European Physical Journal E, 2007In 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.
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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, 2011Riemann-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 +2 more
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The nonlinear Rayleigh‐Stokes problem with Riemann‐Liouville fractional derivative
Mathematical Methods in the Applied Sciences, 2019The 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 with Riemann‐Liouville fractional derivative. We firstly show that the solution operator of the problem
Yong Zhou, Jing Na Wang
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On a backward problem for fractional diffusion equation with Riemann‐Liouville derivative
Mathematical Methods in the Applied Sciences, 2019In 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 +3 more
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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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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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