Fractional Newton-Raphson Method Accelerated with Aitken's Method
, 2021 In the following document, we present a way to obtain the order of convergence of the Fractional Newton-Raphson (F N-R) method, which seems to have an order of convergence at least linearly for the case in which the order $\alpha$ of the derivative is ...
Brambila-Paz, F. +3 more
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On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative
Fractal and Fractional, 2022 The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved.
M. Ruziev, R. Zunnunov
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Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation [PDF]
Open Communications in Nonlinear Mathematical PhysicsIn this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order $x$-derivative.
Jicheng Yu, Yuqiang Feng
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A new Definition of Fractional Derivative and Fractional Integral [PDF]
Kirkuk Journal of Science, 2018 In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
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Fractional Diffusion Based on Riemann-Liouville Fractional Derivatives [PDF]
The Journal of Physical Chemistry B, 2000 11 pages ...
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Analysis of fractional differential systems involving Riemann Liouville fractional derivative
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2020 Summary: This paper is devoted to studying the multiple positive solutions for a system of nonlinear fractional boundary value problems. Our analysis is based upon the Avery Peterson fixed point theorem. In addition, we include an example for the demonstration of our main result.
Batik, Songül, Deren, Fulya Yörük
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Fractional Noether's theorem with classical and Riemann-Liouville derivatives [PDF]
2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012 This is a preprint of a paper whose final and definite form will be published in: 51st IEEE Conference on Decision and Control, December 10-13, 2012, Maui, Hawaii, USA. Article Source/Identifier: PLZ-CDC12.1832.45c07804. Submitted 08-March-2012; accepted 17-July-2012.
Frederico, Gastao S. F. +1 more
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Fractional boundary value problems with Riemann-Liouville fractional derivatives [PDF]
Advances in Difference Equations, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tan, Jingjing, Cheng, Caozong
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Mathematical Modelling and Analysis, 2017 This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first.
Fei Wang, Yongqing Yang
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A possible generalization of acoustic wave equation using the concept of perturbed derivative order [PDF]
, 2013 The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented.
Atangana, Abdon, Kilicman, Adem
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