Fractal variational principles for two different types of fractal plasma models with variable coefficients

Fractals ◽  
2021 ◽  
Author(s):  
Kang-Le Wang ◽  
Hao Wang
Keyword(s):  
Variational Principles ◽  
Variable Coefficients ◽  
Different Types

A NOVEL VARIATIONAL PERSPECTIVE TO FRACTAL WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

Fractals ◽  
2021 ◽  
Author(s):  
XUE-FENG HAN ◽  
KANG-LE WANG
Keyword(s):  
Wave Equations ◽  
Variational Principles ◽  
Variable Coefficients ◽  
Transform Method ◽  
Numerical Examples ◽  
Fractal Models ◽  
Inverse Transform ◽  
Fractal Calculus ◽  
Different Types ◽  
Wave Models

This paper aims at establishing two different types of wave models with unsmooth boundaries by the fractal calculus, and their fractal variational principles are successfully designed by employing the fractal semi-inverse transform method. A new approximate technology is proposed to solve the two fractal models based on the variational principle and fractal two-scale transform method. Finally, two numerical examples show that the proposed method is efficient and accurate, which can be extended to solve different types of fractal models.

scholarly journals Exact Solutions for the Conformable Space-Time Fractional Zeldovich Equation with Time-Dependent Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Sami Injrou
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Combustion Process ◽  
Variable Coefficients ◽  
Space Time ◽  
Time Dependent ◽  
Conformable Fractional Derivative ◽  
Fractional Partial Differential Equations ◽  
Rational Solutions ◽  
Different Types

The aim of this paper is to improve a sub-equation method to solve the space-time fractional Zeldovich equation with time-dependent coefficients involving the conformable fractional derivative. As result, we obtain three families of solutions including the hyperbolic, trigonometric, and rational solutions. These solutions may be helpful to explain several phenomena in chemistry, including the combustion process. The study shows that the used method is effective and reliable and can be utilized as a substitution to construct new solutions of different types of nonlinear conformable fractional partial differential equations (NFPDEs) with variable coefficients.

Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds

1989 ◽  
Vol 206 ◽  
pp. 25-46 ◽  
Author(s):  
Jacob Rubinstein ◽  
S. Torquato
Keyword(s):  
Lower Bounds ◽  
Variational Principles ◽  
Mathematical Formulation ◽  
Upper And Lower Bounds ◽  
Random Boundary ◽  
Slow Viscous Flow ◽  
Fluid Permeability ◽  
Different Types ◽  
Rigorous Bounds ◽  
Random Porous Medium

The problem of the slow viscous flow of a fluid through a random porous medium is considered. The macroscopic Darcy's law, which defines the fluid permeability k, is first derived in an ensemble-average formulation using the method of homogenization. The fluid permeability is given explicitly in terms of a random boundary-value problem. General variational principles, different to ones suggested earlier, are then formulated in order to obtain rigorous upper and lower bounds on k. These variational principles are applied by evaluating them for four different types of admissible fields. Each bound is generally given in terms of various kinds of correlation functions which statistically characterize the microstructure of the medium. The upper and lower bounds are computed for flow interior and exterior to distributions of spheres.

scholarly journals On a curve and a system

2020 ◽  
Vol 5 (3) ◽  
pp. 030-052
Author(s):  
Tuba Ağırman Aydın ◽  
Seda Çayan ◽  
Mehmet Sezer ◽  
Abdullah Mağden
Keyword(s):  
Differential Equations ◽  
Constant Width ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
System Of Differential Equations ◽  
Similar System ◽  
First Order ◽  
Cam Design ◽  
Different Types ◽  
Curves Of Constant Width

Curves of constant width, which have a very special place in many fields such as kinematics, engineering, art, cam design and geometry, are specially discussed under this title. In this study, a system of differential equations characterizing the curves of constant width is examined. This is the system of the first order homogenous differential equations with variable coefficients in the normal form. Approximate solutions of the system, by means of two different polynomial approaches, are calculated and error analysis is made. The obtained results are analyzed on a numerical sample and the best method of approach is determined. This system can also constitute a characterization for different types of curves according to different frames in different spaces. Therefore, this study is important not only for this curve type but also for the geometry of all curves that can be expressed in a similar system.

Application of the Exp-Function Method for Solving Some Evolution Equations with Nonlinear Terms of any Orders

2010 ◽  
Vol 65 (12) ◽  
pp. 1039-1044 ◽  
Author(s):  
Abdelhalim Ebaid
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Evolution Equations ◽  
Burgers Equation ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Full Agreement ◽  
Different Types

In this paper, suitable transformations and a so-called exp-function method are used to obtain different types of exact solutions for some nonlinear evolution equations with variable coefficients and nonlinear terms of any orders. The Korteweg-de Vries equation and the Burgers equation with nonlinear terms of any orders are chosen to show how to apply the exp-function method for these kinds of nonlinear equations. These exact solutions are in full agreement with the previous results obtained by Ebaid and by Zhu.

scholarly journals An efficient algorithm for solving fractional differential equations with boundary conditions

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 6-14 ◽  
Author(s):  
Sertan Alkan ◽  
Kenan Yildirim ◽  
Aydin Secer
Keyword(s):  
Approximate Solution ◽  
Fractional Calculus ◽  
Boundary Value Problem ◽  
Collocation Method ◽  
Present Method ◽  
Fractional Derivatives ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, a sinc-collocation method is described to determine the approximate solution of fractional order boundary value problem (FBVP). The results obtained are presented as two new theorems. The fractional derivatives are defined in the Caputo sense, which is often used in fractional calculus. In order to demonstrate the efficiency and capacity of the present method, it is applied to some FBVP with variable coefficients. Obtained results are compared to exact solutions as well as Cubic Spline solutions. The comparisons can be used to conclude that sinc-collocation method is powerful and promising method for determining the approximate solutions of FBVPs in different types of scenarios.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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