This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves m...This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves may be described by a nonlinear partial differential equation system.The shallow flow model’s primary concept is that the waves are spread out across a large horizontal area before rising vertically.The Fractional Reduced Differential Transform Method(FRDTM)is applied to provide approximate solutions for any given model.This aids in the modelling of the global atmosphere,which has applications in weather and climate forecasting.For the integer-order value(α=1),the FRDTM solution is compared to the precise solution,EADM,and HAM to assess the correctness and efficacy of the proposed technique.展开更多
In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire app...In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations.The acquired results are collated with the exact solutions and other results from literature for integer-orderα,which reveal that the proposed method is effective.Hence,FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.展开更多
This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model....This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model.The present model has been studied on the shallow-water assumption.It is represented by a time-fractional coupled system of non-linear partial differential equations.Solutions to the proposed model for different coastal slopes and ocean depths have been obtained.Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different ordersα.The obtained results are compared with Elzaki Adomian Decomposition Method(EADM)to validate the proposed method for an orderα=1.展开更多
文摘This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves may be described by a nonlinear partial differential equation system.The shallow flow model’s primary concept is that the waves are spread out across a large horizontal area before rising vertically.The Fractional Reduced Differential Transform Method(FRDTM)is applied to provide approximate solutions for any given model.This aids in the modelling of the global atmosphere,which has applications in weather and climate forecasting.For the integer-order value(α=1),the FRDTM solution is compared to the precise solution,EADM,and HAM to assess the correctness and efficacy of the proposed technique.
文摘In this article,non-linear time-fractional diffusion equations are considered to describe oil pollution in the water.The latest technique,fractional reduced differential transform method(FRDTM),is used to ac-quire approximate solutions of the time fractional-order diffusion equation and two cases of Allen-Cahn equations.The acquired results are collated with the exact solutions and other results from literature for integer-orderα,which reveal that the proposed method is effective.Hence,FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.
文摘This paper presents a fractional approach to study the mathematical model of tsunami wave propagation along a coastline of an ocean.Fractional Reduced Differential Transform Method(FRDTM)is used to analyze this model.The present model has been studied on the shallow-water assumption.It is represented by a time-fractional coupled system of non-linear partial differential equations.Solutions to the proposed model for different coastal slopes and ocean depths have been obtained.Effects of coast slope and sea depth variations on tsunami wave velocity and wave amplification have been demonstrated at different time levels and different ordersα.The obtained results are compared with Elzaki Adomian Decomposition Method(EADM)to validate the proposed method for an orderα=1.
