In this article,time fractional Fornberg-Whitham equation of He’s fractional derivative is studied.To transform the fractional model into its equivalent differential equation,the fractional complex transform is used ...In this article,time fractional Fornberg-Whitham equation of He’s fractional derivative is studied.To transform the fractional model into its equivalent differential equation,the fractional complex transform is used and He’s homotopy perturbation method is implemented to get the approximate analytical solutions of the fractional-order problems.The graphs are plotted to analysis the fractional-order mathematical modeling.展开更多
It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obt...It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.展开更多
The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo se...The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.展开更多
In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example...In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.展开更多
Based on the modified homotopy perturbation method （MHPM）, exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact...Based on the modified homotopy perturbation method （MHPM）, exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact solutions. Under suitable initial conditions, the PDE is transformed into an ODE. Some illustrative examples reveal the efficiency of the proposed method.展开更多
In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem in...In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.展开更多
Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes ...Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.展开更多
In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose ...In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.展开更多
In this paper Homotopy Analysis Method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear ...In this paper Homotopy Analysis Method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and Homotopy Perturbation Method(HPM) is also used to solve these equations; finally,approximate solutions by HAM of(2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM, the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3 rd-order approximation solutions by HAM and HPM have great fluctuation.展开更多
In this paper, He’s homotopy perturbation method is utilized to obtainthe analytical solution for the nonlinear natural frequency of functionally gradednanobeam. The functionally graded nanobeam is modeled using the ...In this paper, He’s homotopy perturbation method is utilized to obtainthe analytical solution for the nonlinear natural frequency of functionally gradednanobeam. The functionally graded nanobeam is modeled using the Eringen’s nonlocalelasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearityrelation. The boundary conditions of problem are considered with both sidessimply supported and simply supported-clamped. The Galerkin’s method is utilizedto decrease the nonlinear partial differential equation to a nonlinear second-order ordinarydifferential equation. Based on numerical results, homotopy perturbationmethodconvergence is illustrated. According to obtained results, it is seen that the second termof the homotopy perturbation method gives extremely precise solution.展开更多
The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method.Due to the less accuracy of the classical ...The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method.Due to the less accuracy of the classical elasticity theorems,the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes.Both of the static and dynamic behaviors under static DC and step DC voltages are discussed.The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.展开更多
A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method(HPM).The fractional derivatives are taken in ...A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method(HPM).The fractional derivatives are taken in the Caputo sense.The solutions are given in the form of series with easily computable terms.Numerical results are illustrated through the graph.展开更多
The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with ...The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with a classical perturbation approach,in which the low thrust is assumed to be a perturbation of the nominal Keplerian motion.The homotopy perturbation method provides the analytical(approximate)solution of the dynamical equations in polar form to estimate the corresponding spacecraft propelled trajectory with a short computational time.The accuracy of the analytical results was tested in an orbital-targeting mission scenario.展开更多
The present paper attempts to solve equations in the initial stage and the two-phase flow regime of fuel spray penetration using the HPM-Padétechnique,which is a combination of the homotopy perturbation method(HP...The present paper attempts to solve equations in the initial stage and the two-phase flow regime of fuel spray penetration using the HPM-Padétechnique,which is a combination of the homotopy perturbation method(HPM)and Padéapproximation.At the initial stage,the effects of the droplet drag and the air entrainment were explained while in the two-phase flow stage,the spray droplets had the same velocities as the entrained air.The results for various injection pressures and ambient densities are presented graphically and then discussed upon.The obtained results for these two stages show a good agreement with previously obtained expressions via successive approximations in the available literature.The numerical result indicates that the proposed method is straight forward to implement,efficient and accurate for solving nonlinear equations of fuel spray.展开更多
In this paper, two delay differential systems are considered, namely, a famous model from mathematical biology about the spread of HIV viruses in blood and the advanced Lorenz system from mathematical physics. We then...In this paper, two delay differential systems are considered, namely, a famous model from mathematical biology about the spread of HIV viruses in blood and the advanced Lorenz system from mathematical physics. We then apply the homotopy perturbation method （HPM） to find their approximate solutions. It turns out that the method gives rise to easily obtainable solutions. In addition, residual error functions of the solutions are graphed and it is shown that increasing the parameter n in the method improves the results in both cases.展开更多
In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thi...In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.展开更多
This study examines the intricate occurrences of thermal and solutal Marangoni convection in three-layered flows of viscous fluids,with a particular emphasis on their relevance to renewable energy systems.This researc...This study examines the intricate occurrences of thermal and solutal Marangoni convection in three-layered flows of viscous fluids,with a particular emphasis on their relevance to renewable energy systems.This research examines the flow of a three-layered viscous fluid,considering the combined influence of heat and solutal buoyancy driven Rayleigh-Bénard convection,as well as thermal and solutal Marangoni convection.The homotopy perturbation method is used to examine and simulate complex fluid flow and transport phenomena,providing important understanding of the fundamental physics and assisting in the optimization of various battery configurations.The inquiry examines the primary elements that influence Marangoni convection and its impact on battery performance,providing insights on possible enhancements in energy storage devices.The findings indicate that the velocity profiles shown graphically exhibit a prominent core zone characterized by the maximum speed,which progressively decreases as it approaches the walls of the channel.This study enhances our comprehension of fluid dynamics and the transmission of heat and mass in intricate systems,which has substantial ramifications for the advancement of sustainable energy solutions.展开更多
This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro...This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel,aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios.The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution,utilizing a comprehensive numerical approach.Employing a combination of mathematical modeling techniques,including similarity transformation,this investigation transforms complex partial differential equations into more manageable ordinary ones,subsequently solving them using the homotopy perturbation method.By analyzing the obtained solutions and presenting them graphically,alongside detailed analysis,the study sheds light on the pivotal role of significant parameters in shaping fluid movement and energy distribution.Noteworthy observations reveal a substantial increase in fluid velocity with escalating magnetic parameters,while conversely,a contrasting trend emerges in the temperature distribution,highlighting the intricate relationship between magnetic effects,flow dynamics,and thermal behavior in non-Newtonian fluids.Further,the suction velocity enhance both the local skin friction and Nusselt numbers,whereas theWeissenberg number reduces them,opposite to the effect of the power-law index.展开更多
The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other asso...The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.展开更多
The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytica...The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11561051。
文摘In this article,time fractional Fornberg-Whitham equation of He’s fractional derivative is studied.To transform the fractional model into its equivalent differential equation,the fractional complex transform is used and He’s homotopy perturbation method is implemented to get the approximate analytical solutions of the fractional-order problems.The graphs are plotted to analysis the fractional-order mathematical modeling.
文摘It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.
文摘The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.
文摘In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.
基金Supported by the National Social Science Fund of China (Grant No. 11BTJ011)the Natural Science Foundation Fund of Hunan Province of China (No. 08JJ3004)the Soft Science Foundation of Hunan Province of China (No. 2009ZK4021)
文摘Based on the modified homotopy perturbation method （MHPM）, exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact solutions. Under suitable initial conditions, the PDE is transformed into an ODE. Some illustrative examples reveal the efficiency of the proposed method.
文摘In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.
文摘Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.
文摘In this paper, we have used the homotopy perturbation and the Adomian decomposition methods to study the nonlinear coupled Kortewge-de Vries and shallow water equations. The main objective of this paper is to propose alternative methods of solutions, which do not require small parameters and avoid linearization and physical unrealistic assumptions. The proposed methods give more general exact solutions without much extra effort and the results reveal that the homotopy perturbation and the Adomian decomposition methods are very effective, convenient and quite accurate to the systems of coupled nonlinear equations.
文摘In this paper Homotopy Analysis Method(HAM) is implemented for obtaining approximate solutions of(2+1)-dimensional Navier-Stokes equations with perturbation terms. The initial approximations are obtained using linear systems of the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and Homotopy Perturbation Method(HPM) is also used to solve these equations; finally,approximate solutions by HAM of(2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of the freedom of choice the auxiliary parameter of HAM, the results demonstrate that the rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3 rd-order approximation solutions by HAM and HPM have great fluctuation.
文摘In this paper, He’s homotopy perturbation method is utilized to obtainthe analytical solution for the nonlinear natural frequency of functionally gradednanobeam. The functionally graded nanobeam is modeled using the Eringen’s nonlocalelasticity theory based on Euler-Bernoulli beam theory with von Karman nonlinearityrelation. The boundary conditions of problem are considered with both sidessimply supported and simply supported-clamped. The Galerkin’s method is utilizedto decrease the nonlinear partial differential equation to a nonlinear second-order ordinarydifferential equation. Based on numerical results, homotopy perturbationmethodconvergence is illustrated. According to obtained results, it is seen that the second termof the homotopy perturbation method gives extremely precise solution.
文摘The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method.Due to the less accuracy of the classical elasticity theorems,the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes.Both of the static and dynamic behaviors under static DC and step DC voltages are discussed.The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.
文摘A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method(HPM).The fractional derivatives are taken in the Caputo sense.The solutions are given in the form of series with easily computable terms.Numerical results are illustrated through the graph.
文摘The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with a classical perturbation approach,in which the low thrust is assumed to be a perturbation of the nominal Keplerian motion.The homotopy perturbation method provides the analytical(approximate)solution of the dynamical equations in polar form to estimate the corresponding spacecraft propelled trajectory with a short computational time.The accuracy of the analytical results was tested in an orbital-targeting mission scenario.
文摘The present paper attempts to solve equations in the initial stage and the two-phase flow regime of fuel spray penetration using the HPM-Padétechnique,which is a combination of the homotopy perturbation method(HPM)and Padéapproximation.At the initial stage,the effects of the droplet drag and the air entrainment were explained while in the two-phase flow stage,the spray droplets had the same velocities as the entrained air.The results for various injection pressures and ambient densities are presented graphically and then discussed upon.The obtained results for these two stages show a good agreement with previously obtained expressions via successive approximations in the available literature.The numerical result indicates that the proposed method is straight forward to implement,efficient and accurate for solving nonlinear equations of fuel spray.
文摘In this paper, two delay differential systems are considered, namely, a famous model from mathematical biology about the spread of HIV viruses in blood and the advanced Lorenz system from mathematical physics. We then apply the homotopy perturbation method （HPM） to find their approximate solutions. It turns out that the method gives rise to easily obtainable solutions. In addition, residual error functions of the solutions are graphed and it is shown that increasing the parameter n in the method improves the results in both cases.
文摘In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.
基金Project(52276068)supported by the National Natural Science Foundation of China。
文摘This study examines the intricate occurrences of thermal and solutal Marangoni convection in three-layered flows of viscous fluids,with a particular emphasis on their relevance to renewable energy systems.This research examines the flow of a three-layered viscous fluid,considering the combined influence of heat and solutal buoyancy driven Rayleigh-Bénard convection,as well as thermal and solutal Marangoni convection.The homotopy perturbation method is used to examine and simulate complex fluid flow and transport phenomena,providing important understanding of the fundamental physics and assisting in the optimization of various battery configurations.The inquiry examines the primary elements that influence Marangoni convection and its impact on battery performance,providing insights on possible enhancements in energy storage devices.The findings indicate that the velocity profiles shown graphically exhibit a prominent core zone characterized by the maximum speed,which progressively decreases as it approaches the walls of the channel.This study enhances our comprehension of fluid dynamics and the transmission of heat and mass in intricate systems,which has substantial ramifications for the advancement of sustainable energy solutions.
文摘This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel,aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios.The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution,utilizing a comprehensive numerical approach.Employing a combination of mathematical modeling techniques,including similarity transformation,this investigation transforms complex partial differential equations into more manageable ordinary ones,subsequently solving them using the homotopy perturbation method.By analyzing the obtained solutions and presenting them graphically,alongside detailed analysis,the study sheds light on the pivotal role of significant parameters in shaping fluid movement and energy distribution.Noteworthy observations reveal a substantial increase in fluid velocity with escalating magnetic parameters,while conversely,a contrasting trend emerges in the temperature distribution,highlighting the intricate relationship between magnetic effects,flow dynamics,and thermal behavior in non-Newtonian fluids.Further,the suction velocity enhance both the local skin friction and Nusselt numbers,whereas theWeissenberg number reduces them,opposite to the effect of the power-law index.
基金Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R229), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia。
文摘The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.
文摘The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.
