scholarly journals Conserved vectors with conformable derivative for certain systems of partial differential equations with physical applications

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 164-169
Author(s):  
Maysaa Mohamed Al Qurashi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Nonlinear Partial Differential Equations ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Systems Of Pdes ◽  
First Time ◽  
Conservation Theorem

AbstractIn this paper, we examine conservation laws (Cls) with conformable derivative for certain nonlinear partial differential equations (PDEs). The new conservation theorem is used to the construction of nonlocal Cls for the governing systems of equation. It is worth noting that this paper introduces for the first time, to our knowledge, the analysis for Cls to systems of PDEs with a conformable derivative.

scholarly journals Newly Developed Analytical Scheme and Its Applications to the Some Nonlinear Partial Differential Equations with the Conformable Derivative

2021 ◽  
Vol 5 (4) ◽  
pp. 238
Author(s):  
Li Yan ◽  
Gulnur Yel ◽  
Ajay Kumar ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rational Function ◽  
Analytical Approach ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Analytical Scheme

This paper presents a novel and general analytical approach: the rational sine-Gordon expansion method and its applications to the nonlinear Gardner and (3+1)-dimensional mKdV-ZK equations including a conformable operator. Some trigonometric, periodic, hyperbolic and rational function solutions are extracted. Physical meanings of these solutions are also presented. After choosing suitable values of the parameters in the results, some simulations are plotted. Strain conditions for valid solutions are also reported in detail.

scholarly journals Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Shailesh A. Bhanotar ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensions ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Linear And Nonlinear

In this paper, a novel analytical method for solving nonlinear partial differential equations is studied. This method is known as triple Laplace transform decomposition method. This method is generalized in the sense of conformable derivative. Important results and theorems concerning this method are discussed. A new algorithm is proposed to solve linear and nonlinear partial differential equations in three dimensions. Moreover, some examples are provided to verify the performance of the proposed algorithm. This method presents a wide applicability to solve nonlinear partial differential equations in the sense of conformable derivative.

scholarly journals A Boiti-Leon Pimpinelli equations with time-conformable derivative

2019 ◽  
Vol 9 (3) ◽  
pp. 95-101 ◽  
Author(s):  
Kamal Ait Touchent ◽  
Zakia Hammouch ◽  
Toufik Mekkaoui ◽  
Canan Unlu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Gordon Equation ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
Expansion Technique

In this paper, we derive some new soliton solutions to $(2+1)$-Boiti-Leon Pempinelli equations with conformable derivative by using an expansion technique based on the Sinh-Gordon equation. The obtained solutions have different expression such as trigonometric, complex and hyperbolic functions. This powerful and simple technique can be used to investigate solutions of other  nonlinear partial differential equations.

scholarly journals New extended generalized Kudryashov method for solving three nonlinear partial differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Reham M.A. Shohib ◽  
Mohamed E.M. Alngar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Nonlinear Partial Differential Equations ◽  
Magnetized Plasma ◽  
Ion Acoustic Waves ◽  
Partial Differential ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
First Time

New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.

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