Results 11 to 20 of about 599,088 (208)

On the Approximate Controllability of Fractional Evolution Equations with Generalized Riemann-Liouville Fractional Derivative

Journal of Function Spaces, 2015
We discuss the approximate controllability of fractional evolution equations involving generalized Riemann-Liouville fractional derivative. The results are obtained with the help of the theory of fractional calculus, semigroup theory, and the Schauder ...
N. I. Mahmudov, M. A. McKibben
core   +4 more sources

On a Generic Fractional Derivative Associated with the Riemann–Liouville Fractional Integral

Axioms
In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann–Liouville fractional integral.
Yuri Luchko
core   +3 more sources

Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory

Mathematics, 2023
In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually using ...
Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
doaj   +1 more source

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

Application of Riemann–Liouville Derivatives on Second-Order Fractional Differential Equations: The Exact Solution

Fractal and Fractional, 2023
This paper applies two different types of Riemann–Liouville derivatives to solve fractional differential equations of second order. Basically, the properties of the Riemann–Liouville fractional derivative depend mainly on the lower bound of the integral ...
Abdulrahman B. Albidah
doaj   +1 more source

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

Evaluating an Improper Fractional Integral Based on Jumarie's Modified Riemann-Liouville Fractional Calculus

, 2023
: In this paper, based on Jumarie’s modified Riemann-Liouville (R-L) fractional calculus, we find the solution of some type of improper fractional integral.
Chii-Huei Yu
core   +1 more source

Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation [PDF]

Open Communications in Nonlinear Mathematical Physics
In 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
doaj   +1 more source

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
doaj   +1 more source