Results 1 to 10 of about 12,553 (141)

Formation of advanced soliton dynamics through the M-fractional regularized long-wave equation. [PDF]

Sci Rep
Hossain MM, Roshid HO, Ullah MS, Sheikh MAN.   +3 more
europepmc   +1 more source

On the fractional derivatives at extrema points [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2012
We correct a recent result concerning the fractional derivative at extrema points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extrema points.
Mohammed Al-Refai
doaj   +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

Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations

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, Stepan Tersian, Radoslava Terzieva   +2 more
doaj   +1 more source

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 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 ...
Torres-Hernandez, A., Brambila-Paz, F., Iturrarán-Viveros, U., Caballero-Cruz, R.   +3 more
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

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
core   +3 more sources

Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems

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
doaj   +1 more source