scholarly journals A Variety of Explicit Exact and Soliton Type Solutions of Conformable Fractional Equal-Width Equations

2018 ◽  
Author(s):  
Alper Korkmaz ◽  
Asim Zafar ◽  
Hadi Rezazadeh
Keyword(s):  
Fluid Dynamics ◽  
Surface Waves ◽  
Space Time ◽  
Function Approach ◽  
Hyperbolic Function ◽  
Trigonometric Functions ◽  
Conformable Derivative ◽  
Wave Type

Exact and soliton type solutions have great importance in propagation of surface waves, fluid dynamics, optics, and many other elds of nonlinear sciences. In this study, the explicit and exact soliton type solutions for two space-time fractional Equal- Width (FEW) equations with conformable derivative are procured via the hyperbolic function approach. The wave type solutions are represented in some hyperbolic and trigonometric functions.

scholarly journals Rational exponential solutions of conformable space-time fractional equal-width equations

2019 ◽  
Vol 8 (1) ◽  
pp. 350-355 ◽  
Author(s):  
Asim Zafar
Keyword(s):  
Exact Solutions ◽  
Fractional Order ◽  
Symbolic Computation ◽  
Space Time ◽  
Function Approach ◽  
Conformable Derivative ◽  
Nonlinear Odes ◽  
New Exact Solutions ◽  
Conformable Derivatives ◽  
The Way

Abstract In this paper, the rational exponential solutions of two space-time fractional equal-width (FEW) equations are explored in the conformable derivative sense. The way to reach explicit exact solutions is to transform the fractional order PDEs into a nonlinear ODEs of discrete order through some properties of conformable derivatives and a fractional complex transforms. The subsequent equations have been elucidated by employing the exp a function approach. Some new exact solutions of the said equations are effectively formulated and graphically conveyed with the aid of symbolic computation in Mathematica and MATLAB respectively.

scholarly journals A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ji Juan-Juan ◽  
Guo Ye-Cai ◽  
Zhang Lan-Fang ◽  
Zhang Chao-Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Table Lookup ◽  
Exact Analytical Solutions ◽  
Function Solution

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

scholarly journals COVARIANT WIGNER FUNCTION APPROACH TO THE BOLTZMANN EQUATION FOR MIXING FERMIONS IN CURVED SPACE–TIME

2003 ◽  
Vol 18 (24) ◽  
pp. 4469-4484 ◽  
Author(s):  
KAZUHIRO YAMAMOTO
Keyword(s):  
Boltzmann Equation ◽  
Wigner Function ◽  
Gravitational Effect ◽  
Space Time ◽  
Function Approach ◽  
Order Effects ◽  
Relativistic Limit ◽  
Curved Space ◽  
The Boltzmann Equation ◽  
Flavor Oscillation

Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved space–time. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to ℏ reproduces the previous result which was derived in the relativistic limit on the Minkowski background space–time. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obtained by solving the Boltzmann equation. Higher order effects of the ℏ-expansion are also briefly discussed.

scholarly journals Study of fluid dynamics at the boundary wall of a microchannel by Bloch surface waves

2019 ◽  
Vol 44 (8) ◽  
pp. 1932
Author(s):  
A. Occhicone ◽  
A. Sinibaldi ◽  
F. Sonntag ◽  
P. Munzert ◽  
N. Danz ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Surface Waves ◽  
Boundary Wall

scholarly journals ON THE COMPLEX MIXED DARK-BRIGHT WAVE DISTRIBUTIONS TO SOME CONFORMABLE NONLINEAR INTEGRABLE MODELS

Fractals ◽  
2021 ◽  
pp. 2240018
Author(s):  
ARMANDO CIANCIO ◽  
GULNUR YEL ◽  
AJAY KUMAR ◽  
HACI MEHMET BASKONUS ◽  
ESIN ILHAN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Expansion Method ◽  
Research Paper ◽  
Trigonometric Function ◽  
Integrable Models ◽  
Hyperbolic Function ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Wave Solutions

In this research paper, we implement the sine-Gordon expansion method to two governing models which are the (2+1)-dimensional Nizhnik–Novikov–Veselov equation and the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. We use conformable derivative to transform these nonlinear partial differential models to ordinary differential equations. We find some wave solutions having trigonometric function, hyperbolic function. Under the strain conditions of these solutions obtained in this paper, various simulations are plotted.

scholarly journals Solution of Moving Boundary Space-Time Fractional Burger’s Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
E. A.-B. Abdel-Salam ◽  
E. A. Yousif ◽  
Y. A. S. Arko ◽  
E. A. E. Gumma
Keyword(s):  
Moving Boundary ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Space Time ◽  
Hyperbolic Function ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Hyperbolic Function Solutions ◽  
First Time ◽  
Boundary Space

The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.

scholarly journals SUPERSYMMETRIC STRING WAVES

1994 ◽  
Vol 03 (01) ◽  
pp. 149-152
Author(s):  
ERIC BERGSHOEFF
Keyword(s):  
Plane Wave ◽  
Effective Action ◽  
Space Time ◽  
Gauge Fields ◽  
Wave Type ◽  
Axion Field ◽  
String Corrections ◽  
Crucial Property

We present plane-wave-type solutions to the superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a generalization of the Brinkmann metric. A crucial property of the solutions is a conspiracy between the metric and the axion field. Furthermore, due to a relation between the geometry and the gauge fields, the α′ string corrections to the effective on-shell action and to the solutions themselves vanish. We call these solutions supersymmetric string waves.

scholarly journals A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics

2020 ◽  
Vol 23 (1-4) ◽  
Author(s):  
Joshua Christopher ◽  
Robert D. Falgout ◽  
Jacob B. Schroder ◽  
Stephen M. Guzik ◽  
Xinfeng Gao
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Parallel Algorithm ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Space Time

scholarly journals Ratios of forces and forces moments as dynamic similarity criteria of various phenomena occurring in wind engineering, snow engineering and fluid dynamics

2019 ◽  
Vol 17 (4) ◽  
pp. 121-140
Author(s):  
Andrzej Flaga
Keyword(s):  
Fluid Dynamics ◽  
Surface Waves ◽  
Contact Problems ◽  
Wind Engineering ◽  
Similarity Criteria ◽  
Solid Contact ◽  
Dynamic Similarity

The work concerns dynamic similarity criteria of various phenomena occurring in wind engineering, snow engineering and fl uid dynamics derived from ratios of forces and forces moments affecting these phenomena. Derived and analyzed in part I dynamic similarity criteria, mainly concern the following steady problems: 1. Fluid fl ows and fl ows past objects ; 2. Fluid-solid contact problems; 3. Problems of a solid fl oating on a fl uid with and without of the surface waves.

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