scholarly journals A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

2021 ◽  
Vol 11 (3) ◽  
pp. 52-67
Author(s):  
Pundikala Veeresha ◽  
Mehmet Yavuz ◽  
Chandrali Baishya
Keyword(s):  
Fractional Order ◽  
Nonlinear Models ◽  
Kdv Equation ◽  
Physical Nature ◽  
Critical Flow ◽  
Fractional Operators ◽  
Power Law Distribution ◽  
Analysis Scheme ◽  
De Vries ◽  
Homotopy Analysis

The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

A novel approach for nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law

2020 ◽  
Vol 37 (6) ◽  
pp. 1865-1897 ◽  
Author(s):  
P. Veeresha ◽  
D.G. Prakasha ◽  
Jagdev Singh
Keyword(s):  
Nonlinear Equations ◽  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Content Type ◽  
Physical Behaviour ◽  
Special Cases ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
The Future ◽  
Homotopy Analysis

Purpose The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM). Design/methodology/approach The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. Originality/value To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag–Leffler Kernel

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Order Model ◽  
Science And Engineering ◽  
Transform Method ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis

Abstract In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method (q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag–Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.

scholarly journals Fractional System of Korteweg-De Vries Equations via Elzaki Transform

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 673
Author(s):  
Wenfeng He ◽  
Nana Chen ◽  
Ioannis Dassios ◽  
Nehad Ali Shah ◽  
Jae Dong Chung
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Hybrid Technique ◽  
Transform Method ◽  
De Vries ◽  
In Series ◽  
Analytical Result ◽  
Approximate Result ◽  
Good Agreement

In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined. The iteration transform method solutions are obtained in series form to analyze the analytical results of fractional-order coupled Korteweg-de Vries equations. To understand the analytical procedure of Iteration transform method, some numerical problems are presented for the analytical result of fractional-order coupled Korteweg-de Vries equations. It is also demonstrated that the current technique’s solutions are in good agreement with the exact results. The numerical solutions show that only a few terms are sufficient for obtaining an approximate result, which is efficient, accurate, and reliable.

scholarly journals ITERATIVE METHOD APPLIED TO THE FRACTIONAL NONLINEAR SYSTEMS ARISING IN THERMOELASTICITY WITH MITTAG-LEFFLER KERNEL

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040040 ◽  
Author(s):  
WEI GAO ◽  
P. VEERESHA ◽  
D. G. PRAKASHA ◽  
BILGIN SENEL ◽  
HACI MEHMET BASKONUS
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Order Model ◽  
Science And Engineering ◽  
One Dimensional ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis ◽  
The One

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with [Formula: see text]-homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

scholarly journals A reliable analytical technique for fractional Caudrey-Dodd-Gibbon equation with Mittag-Leffler kernel

2020 ◽  
Vol 9 (1) ◽  
pp. 319-328 ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Order Model ◽  
Science And Engineering ◽  
Transform Method ◽  
Analytical Technique ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis

AbstractThe pivotal aim of the present work is to find the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q-homotopy analysis transform method (q-HATM). The considered technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the projected fractional-order model. In order to illustrate and validate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to examine the nature of nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

scholarly journals Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
R. I. Nuruddeen ◽  
Khalid K. Ali ◽  
Lawal Muhammad ◽  
M. S. Osman ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Mathematical Physics ◽  
Order Derivative ◽  
Conformable Fractional Derivative ◽  
Fractional Order Derivative ◽  
De Vries ◽  
Fifth Order ◽  
2D And 3D

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

Nonlocal Symmetries, Explicit Solutions, and Wave Structures for the Korteweg–de Vries Equation

2016 ◽  
Vol 71 (8) ◽  
pp. 735-740
Author(s):  
Zheng-Yi Ma ◽  
Jin-Xi Fei
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Elliptic Functions ◽  
Group Method ◽  
Physical Interaction ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
The Kdv Equation ◽  
De Vries ◽  
Exact Invariant

AbstractFrom the known Lax pair of the Korteweg–de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.

scholarly journals Evaluation of a FO-PID Controller in a Buck DC/DC Converter Model

2019 ◽  
pp. 1-8
Author(s):  
German A Munoz-Hernandez ◽  
Ana S Damian-Mora ◽  
Jose Ramirez-Espinoza ◽  
Jesus Chavez-Galan
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Nonlinear Models ◽  
Electrical Energy ◽  
Degree Of Freedom ◽  
Pid Controllers ◽  
Adaptive Controllers ◽  
Operational Conditions ◽  
Linear And Nonlinear ◽  
Common Device

The applications of electrical energy converters are wide. It is a common device that can be found in almost every apparatus, both industrial and domestic. This work will deal with linear and nonlinear models of DC/DC converters. Those models will used to probe, by simulation, classic and advance controllers. PID controllers have shown a good response regulating DC/DC converters, for that reason the inclusion of two more degree of freedom due to the Integral and derivative of Fractional Order, could improve the performance of these controllers. Furthermore, Piecewise modeling can be useful to obtain adaptive controllers whose parameters change at different operational conditions.

Sign in / Sign up

Export Citation Format

Share Document