scholarly journals Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3253
Author(s):  
Abdulmohsen D. Alruwaili ◽  
Aly R. Seadawy ◽  
Asghar Ali ◽  
Sid Ahmed O. Beinane
Keyword(s):  
Differential Equation ◽  
Travelling Wave ◽  
Space Time ◽  
Successful Implementation ◽  
Mathematical Methods ◽  
Wave Solutions ◽  
Complex Transformation ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Solitary Travelling Wave

The aim of this work is to build novel analytical wave solutions of the nonlinear space-time fractional (2+1)-dimensional breaking soliton equations, with regards to the modified Riemann–Liouville derivative, by employing mathematical schemes, namely, the improved simple equation and modified F-expansion methods. We used the fractional complex transformation of the concern fractional differential equation to convert it for the solvable integer order differential equation. After the successful implementation of the presented methods, a comprehensive class of novel and broad-ranging exact and solitary travelling wave solutions were discovered, in terms of trigonometric, rational and hyperbolic functions. Hence, the present methods are reliable and efficient for solving nonlinear fractional problems in mathematics physics.

Study on Fractional Differential Equations with Modified Riemann–Liouville Derivative via Kudryashov Method

2019 ◽  
Vol 20 (5) ◽  
pp. 511-516
Author(s):  
Esin Aksoy ◽  
Ahmet Bekir ◽  
Adem C Çevikel
Keyword(s):  
Differential Equations ◽  
Kdv Equation ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Fractional Equations ◽  
Complex Transformation ◽  
Liouville Derivative ◽  
Kudryashov Method ◽  
Regularized Long Wave Equation ◽  
Fractional Differential

AbstractIn this work, the Kudryashov method is handled to find exact solutions of nonlinear fractional partial differential equations in the sense of the modified Riemann–Liouville derivative as given by Guy Jumarie. Firstly, these fractional equations can be turned into another nonlinear ordinary differential equations by fractional complex transformation. Then, the method is applied to solve the space-time fractional Symmetric Regularized Long Wave equation and the space-time fractional generalized Hirota–Satsuma coupled KdV equation. The obtained solutions include generalized hyperbolic functions solutions.

Solitary Wave and other Solutions of Nonlinear Space-Time Fractional Differential Equation Systems

2018 ◽  
pp. 515-522
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Expansion Method ◽  
Travelling Wave ◽  
Boussinesq System ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Fractional System ◽  
Partial Fractional Differential Equation

In this study, we have successfully found some travelling wave solutions of the variant Boussinesq system and fractional system of two-dimensional Burgers' equations of fractional order by using the -expansion method. These exact solutions contain hyperbolic, trigonometric and rational function solutions. The fractional complex transform is generally used to convert a partial fractional differential equation (FDEs) with modified Riemann-Liouville derivative into ordinary differential equation. We showed that the considered transform and method are very reliable, efficient and powerful in solving wide classes of other nonlinear fractional order equations and systems.

scholarly journals Construction of abundant novel analytical solutions of the space–time fractional nonlinear generalized equal width model via Riemann–Liouville derivative with application of mathematical methods

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 657-668
Author(s):  
Aly R. Seadawy ◽  
Asghar Ali ◽  
Saad Althobaiti ◽  
Khaled El-Rashidy
Keyword(s):  
Differential Equation ◽  
Soliton Solutions ◽  
Magnetic Interaction ◽  
Space Time ◽  
Auxiliary Equation ◽  
Mathematical Methods ◽  
Nonlinear Fractional Differential Equation ◽  
Dispersive Waves ◽  
Composite Function ◽  
Liouville Derivative

Abstract The space–time fractional generalized equal width (GEW) equation is an imperative model which is utilized to represent the nonlinear dispersive waves, namely, waves flowing in the shallow water strait, one-dimensional wave origination escalating in the nonlinear dispersive medium approximation, gelid plasma, hydro magnetic waves, electro magnetic interaction, etc. In this manuscript, we probe advanced and broad-spectrum wave solutions of the formerly betokened model with the Riemann–Liouville fractional derivative via the prosperously implementation of two mathematical methods: modified elongated auxiliary equation mapping and amended simple equation methods. The nonlinear fractional differential equation (NLFDE) is renovated into ordinary differential equation by the composite function derivative and the chain rule putting together along with the wave transformations. We acquire several types of exact soliton solutions by setting specific values of the personified parameters. The proposed schemes are expedient, influential, and computationally viable to scrutinize notches of NLFDEs.

scholarly journals Solutions of the perturbed KdV equation for convecting fluids by factorizations

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Octavio Cornejo-Pérez ◽  
Haret Rosu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Second Order ◽  
Travelling Wave Solutions ◽  
Second Order Differential Equation ◽  
Wave Solutions ◽  
Perturbed Kdv Equation

AbstractIn this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.

Sign in / Sign up

Export Citation Format

Share Document