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A new fractional analytical approach via a modified Riemann–Liouville derivative

Applied Mathematics Letters, 2012
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Yasir Khan, Qingbiao Wu, Naeem Faraz
exaly   +3 more sources

On the k-Riemann-Liouville fractional derivative [PDF]

International Journal of Contemporary Mathematical Sciences, 2013
The aim of this paper is to introduce an alternative denition for the k-Riemann-Liouville fractional derivative given in [6] and whose advantage is that it is the left inverse of the corresponding of k-RiemannLiouville fractional integral operator introduced by [5].
L. G. Romero, L. L. Luque, G. A. Dorrego, R. A. Cerutti   +3 more
core   +6 more sources

On Conformable, Riemann-Liouville, and Caputo fractional derivatives

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 of the solutions.
Bambang Hendriya Guswanto, Leony Rhesmafiski Andini, Triyani Triyani   +2 more
openaire   +3 more sources

Stability analysis of fractional differential system with Riemann–Liouville derivative

Mathematical and Computer Modelling, 2010
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Changpin Li, Ravi P Agarwal, Patricia J Y Wong   +2 more
exaly   +3 more sources

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
exaly   +2 more sources

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.
Gastão S. F. Frederico, Delfim F. M. Torres   +1 more
openaire   +2 more sources

Fractional Sobolev Spaces via Riemann-Liouville Derivatives [PDF]

Journal of Function Spaces and Applications, 2013
Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of some imbeddings ...
Dariusz Idczak, Stanisław Walczak
openaire   +3 more sources

Generalized Extended Riemann-Liouville Type Fractional Derivative Operator

Kragujevac Journal of Mathematics, 2023
In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform and integral representations are obtained for these ...
Abbas, Hafida, Azzouz, Abdelhalim, Zahaf, Mohammed Brahim, Belmekki, Mohammed   +3 more
openaire   +2 more sources

Cauchy problem for the equations with fractional of Riemann-Liouville derivatives

Doklady of the National Academy of Sciences of Belarus, 2020
Summary: In this article, we study the question of the solvability of an analogue of the Cauchy problem for ordinary differential equations with fractional Riemann-Liouville derivatives on the unbounded right-hand side in certain function spaces. The solvability conditions of the problem under consideration in given function spaces, as well as the ...
Zabreĭko, Petr P., Ponomareva, Svetlana Vladimirovna   +1 more
openaire   +3 more sources

Fractional Diffusion Based on Riemann-Liouville Fractional Derivatives [PDF]

The Journal of Physical Chemistry B, 2000
11 pages ...
openaire   +2 more sources