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An Alternative Definition for the k-Riemann-Liouville Fractional Derivative [PDF]
Applied Mathematical Sciences, 2015 Copyright c © 2014 Gustavo Abel Dorrego. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly ...
Dorrego, Gustavo +2 more
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On Conformable, Riemann-Liouville, and Caputo fractional derivatives [PDF]
Bulletin of Applied Mathematics and Mathematics Education, 2022 This article compares conformable fractional Derivative with Riemann-Liouville and Caputo fractional derivative by comparing solutions to fractional ordinary differential equations involving the three fractional derivatives via the numerical simulations ...
Guswanto, Bambang Hendriya +2 more
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Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations [PDF]
Fractal and Fractional, 2021 A system of nonlinear fractional differential equations with the Riemann–Liouville fractional derivative is considered. Lipschitz stability in time for the studied equations is defined and studied.
Snezhana Hristova +2 more
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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.
Kwok Sau Fa
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Integral-Type Fractional Equations with a Proportional Riemann–Liouville Derivative [PDF]
Journal of Mathematics, 2021 In this paper, we present the necessary conditions where integral-type fractional equations with a proportional Riemann–Liouville derivative have a unique solution.
Nabil Mlaiki
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Advances in Difference Equations, 2018 Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and ...
M. Shadab +2 more
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Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem [PDF]
Abstract and Applied Analysis, 2014 By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under ...
Wenzhe Xie, Jing Xiao, Zhiguo Luo
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The first or higher order Riemann–Liouville (R‐L) type fractional derivatives are studied. The relations between the R‐L type fractional derivatives and the classical R‐L fractional derivatives are obtained and the spaces of functions on which the R‐L type fractional derivatives exist are provided.
Kunquan Lan
wiley +2 more sources
On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative [PDF]
International Journal of Differential Equations, 2012 Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative.
Mehmet Merdan
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Extended Riemann-Liouville fractional derivative operator and its applications [PDF]
, 2015 Many authors have introduced and investigated certain extended fractional derivative operators. The main object of this paper is to give an extension of the Riemann-Liouville fractional derivative operator with the extended Beta function given by ...
Agarwal, Praveen +2 more
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