In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutio...In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation(CEWE) and the space-time fractional coupled modified equal width wave equation(CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.展开更多
In this paper, the modified Kudryashov method is employed to find the traveling wave solutions of two well-known space-time fractional partial differential equations, namely the Zakharov Kuznetshov Benjamin Bona Mahon...In this paper, the modified Kudryashov method is employed to find the traveling wave solutions of two well-known space-time fractional partial differential equations, namely the Zakharov Kuznetshov Benjamin Bona Mahony equation and Kolmogorov Petrovskii Piskunov equation, and as a helping tool, the sense of modified Riemann-Liouville derivative is also used. The propagation properties of obtained solutions are investigated where the graphical representations and justifications of the results are done by mathematical software Maple.展开更多
The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and engineering.The conformable time fractional(2+1)-dimensional extended Zakharov-Kuz...The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and engineering.The conformable time fractional(2+1)-dimensional extended Zakharov-Kuzetsov equation(EZKE),coupled space-time fractional(2+1)-dimensional dispersive long wave equation(DLWE)and space-time fractional(2+1)-dimensional Ablowitz-Kaup-Newell-Segur(AKNS)equation are considered to investigate such physical phenomena.The modified Kudryashov method along with the properties of conformable and modified Riemann-Liouville derivatives is employed to construct the oblique wave solutions of the considered equations.The obtained results may be useful for better understanding the nature of internal oblique propagating wave dynamics in ocean engineering.展开更多
Exact solutions to conformable time fractional (3+1)-dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integ...Exact solutions to conformable time fractional (3+1)-dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE.The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo–Miwa, the Zakharov–Kuznetsov, and the modified Zakharov–Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.展开更多
In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant r...In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.展开更多
The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of pr...The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified Sawada-Kotera equations.As a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada-Kotera equation.We have also presented the numerical simulations for time-fractional fifth-order modified Sawada-Kotera equation by means of three dimensional plots.展开更多
In this study,the fifth-order modified Korteweg-de Vries(F-MKdV)equation is first addressed using Hi-rota’s bilinear method.Thereafter,the exact and approximative solutions of the generalized form of the F-MKdV equat...In this study,the fifth-order modified Korteweg-de Vries(F-MKdV)equation is first addressed using Hi-rota’s bilinear method.Thereafter,the exact and approximative solutions of the generalized form of the F-MKdV equation are investigated using the modified Kudryashov method,the Riccati equation and its Backlund transformation method,the solitary wave ansatz method,and the homotopy perturbation trans-form method(HPTM).As a result,solitons,breather,and solitary wave solutions are derived from these methods.In particular,we obtain some new solutions such as the dark soliton,bright soliton,singular soliton,periodic trigonometric,exponential,hyperbolic,and rational solutions.The constraint conditions associated with the resulting solutions are also discussed in detail.The HPTM is employed to construct approximate solutions to the aforementioned generalized model due to its strong nonlinear terms and only a few terms are required to obtain accurate solutions.These findings may help to understand com-plex nonlinear phenomena.展开更多
In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1...In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model representing the wave propagation through incompressible fluids.The linearization of the wave structure in shallow water necessitates more critical wave capacity conditions than it does in deep water,and the strong nonlinear properties are perceptible.Some novel travelling wave solutions have been observed including solitons,kink,periodic and rational solutions with the aid of the latest computing tools such as Mathematica or Maple.The physical and analytical properties of several families of closed-form solutions or exact solutions and rational form function solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model problem are examined using Mathematica.展开更多
In this work,we studied a(2+1)-dimensional Sawada-Kotera equation(SKE).This model depicts non-linear wave processes in shallow water,fluid dynamics,ion-acoustic waves in plasmas and other phe-nomena.A couple of well-e...In this work,we studied a(2+1)-dimensional Sawada-Kotera equation(SKE).This model depicts non-linear wave processes in shallow water,fluid dynamics,ion-acoustic waves in plasmas and other phe-nomena.A couple of well-established techniques,the Bäcklund transformation based on the modified Kudryashov method,and the Sardar-sub equation method are applied to obtain the soliton wave solution to the(2+1)-dimensional structure.To illustrate the behavior of the nonlinear model in an appealing fashion,a variety of travelling wave solutions are formed,such as contour,2D,and 3D plots.The pro-posed approaches are proved more convenient and dominant for getting analytical solutions and can also be implemented to a variety of physical models representing nonlinear wave phenomena.展开更多
文摘In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation(CEWE) and the space-time fractional coupled modified equal width wave equation(CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels.
文摘In this paper, the modified Kudryashov method is employed to find the traveling wave solutions of two well-known space-time fractional partial differential equations, namely the Zakharov Kuznetshov Benjamin Bona Mahony equation and Kolmogorov Petrovskii Piskunov equation, and as a helping tool, the sense of modified Riemann-Liouville derivative is also used. The propagation properties of obtained solutions are investigated where the graphical representations and justifications of the results are done by mathematical software Maple.
文摘The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and engineering.The conformable time fractional(2+1)-dimensional extended Zakharov-Kuzetsov equation(EZKE),coupled space-time fractional(2+1)-dimensional dispersive long wave equation(DLWE)and space-time fractional(2+1)-dimensional Ablowitz-Kaup-Newell-Segur(AKNS)equation are considered to investigate such physical phenomena.The modified Kudryashov method along with the properties of conformable and modified Riemann-Liouville derivatives is employed to construct the oblique wave solutions of the considered equations.The obtained results may be useful for better understanding the nature of internal oblique propagating wave dynamics in ocean engineering.
文摘Exact solutions to conformable time fractional (3+1)-dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE.The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo–Miwa, the Zakharov–Kuznetsov, and the modified Zakharov–Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.
文摘In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.
文摘The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified Sawada-Kotera equations.As a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada-Kotera equation.We have also presented the numerical simulations for time-fractional fifth-order modified Sawada-Kotera equation by means of three dimensional plots.
文摘In this study,the fifth-order modified Korteweg-de Vries(F-MKdV)equation is first addressed using Hi-rota’s bilinear method.Thereafter,the exact and approximative solutions of the generalized form of the F-MKdV equation are investigated using the modified Kudryashov method,the Riccati equation and its Backlund transformation method,the solitary wave ansatz method,and the homotopy perturbation trans-form method(HPTM).As a result,solitons,breather,and solitary wave solutions are derived from these methods.In particular,we obtain some new solutions such as the dark soliton,bright soliton,singular soliton,periodic trigonometric,exponential,hyperbolic,and rational solutions.The constraint conditions associated with the resulting solutions are also discussed in detail.The HPTM is employed to construct approximate solutions to the aforementioned generalized model due to its strong nonlinear terms and only a few terms are required to obtain accurate solutions.These findings may help to understand com-plex nonlinear phenomena.
文摘In this article,the(1/G')-expansion method,the Bernoulli sub-ordinary differential equation method and the modified Kudryashov method are implemented to construct a variety of novel analytical solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model representing the wave propagation through incompressible fluids.The linearization of the wave structure in shallow water necessitates more critical wave capacity conditions than it does in deep water,and the strong nonlinear properties are perceptible.Some novel travelling wave solutions have been observed including solitons,kink,periodic and rational solutions with the aid of the latest computing tools such as Mathematica or Maple.The physical and analytical properties of several families of closed-form solutions or exact solutions and rational form function solutions to the(3+1)-dimensional Boiti-Leon-Manna-Pempinelli model problem are examined using Mathematica.
文摘In this work,we studied a(2+1)-dimensional Sawada-Kotera equation(SKE).This model depicts non-linear wave processes in shallow water,fluid dynamics,ion-acoustic waves in plasmas and other phe-nomena.A couple of well-established techniques,the Bäcklund transformation based on the modified Kudryashov method,and the Sardar-sub equation method are applied to obtain the soliton wave solution to the(2+1)-dimensional structure.To illustrate the behavior of the nonlinear model in an appealing fashion,a variety of travelling wave solutions are formed,such as contour,2D,and 3D plots.The pro-posed approaches are proved more convenient and dominant for getting analytical solutions and can also be implemented to a variety of physical models representing nonlinear wave phenomena.
