Results 111 to 120 of about 40,676 (212)

Discretization of Fractional Differential Equations by a Piecewise Constant Approximation

, 2016
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a dynamical ...
Angstmann, Christopher N, Henry, Bruce I, McGann, Anna V   +2 more
core  

On Efficient Method for System of Fractional Differential Equations

Advances in Difference Equations, 2011
The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations. In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the ...
Jamil Muhammad, Khan NajeebAlam, Ara Asmat, Khan Nasir-Uddin   +3 more
doaj  

On some explicit solitary wave patterns for a generalized nonlinear reaction–diffusion equation with conformable temporal fractional derivative

Partial Differential Equations in Applied Mathematics
Soliton solutions of a (2+1)-dimensional reaction–diffusion problem are derived in the present work using the generalized Riccati equation mapping method.
Muhammad Jawaz, Jorge E. Macías-Díaz, Syed A. Aqeel, Nauman Ahmed, Muhammad Z. Baber, María G. Medina-Guevara   +5 more
doaj   +1 more source

Global differential geometry: An introduction for control engineers [PDF]

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis.
Doolin, B. F., Martin, C. F.
core   +1 more source

On the comparative analysis for the fractional solitary wave profiles to the recently developed nonlinear system

Ain Shams Engineering Journal
We study the comparative exact solutions of the Kairat-II equation describing the physical behaviors of nonlinear systems. The newly introduced Kairat equation has numerous applications in the fields of plasma physics, optical communications ...
Usman Younas, Jan Muhammad, Naila Nasreen, Aziz Khan, Thabet Abdeljawad   +4 more
doaj   +1 more source

A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains

Computational and Applied Mathematics, 2019
H. Azin, F. Mohammadi, J. Machado
semanticscholar   +1 more source

Anharmonic Solutions to the Riccati equation and elliptic modular functions

We study algebraic solutions of the Riccati equation over the field of rational functions $\mathbb C(t)$, and over the elliptic function field $\mathbb C(\wp,\wp^\prime)$
Sebbar, Ahmed, Wone, Oumar
core  

A Generalization of the Eulerian Numbers

, 2017
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral representations of some ...
Rzadkowski, Grzegorz, Urlinska, Malgorzata   +1 more
core  

New Interaction Patterns for the Truncated M-Fractional Kadomtsev–Petviashvili Equation in High-Dimensional Space

Fractal and Fractional
A truncated M-fractional Kadomtsev–Petviashvili (KP) equation in high-dimensional space has been proposed. The model provides the oretical support for studying the interaction patterns among waves.
Lihua Zhang, Shuqi Chong, Hongbing Jiao, Bo Shen, Gangwei Wang   +4 more
doaj   +1 more source

Weakly nonassociative algebras, Riccati and KP hierarchies

, 2007
It has recently been observed that certain nonassociative algebras (called "weakly nonassociative", WNA) determine, via a universal hierarchy of ordinary differential equations, solutions of the KP hierarchy with dependent variable in an associative ...
Dimakis, Aristophanes, Muller-Hoissen, Folkert   +1 more
core   +2 more sources