We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gor...We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.展开更多
The current study deals with exact soliton solutions for Schrödinger-Hirota(SH)equation via two modi-fied integration methods.Those methods are known as the improved(G/G)-expansion method and the Kudryashov metho...The current study deals with exact soliton solutions for Schrödinger-Hirota(SH)equation via two modi-fied integration methods.Those methods are known as the improved(G/G)-expansion method and the Kudryashov method.This model is a generalized version of the nonlinear Schrödinger(NLS)equation with higher order dispersion and cubic nonlinearity.It can be considered as a more accurate approximation than the NLS equation in explaining wave propagation in the ocean and optical fibers.A novel deriva-tive operator named as the conformable truncated M-fractional is used to study the above mentioned model.The obtained results can be used in describing the Schrödinger-Hirota equation in some better way.Moreover the obtained results are verified through symbolic computational software.Also,the ob-tained results show that the suggested approaches have broaden capacity to secure some new soliton type solutions for the fractional differential equations in an effective way.In the end,the results are also explained through their graphical representations.展开更多
文摘We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.
文摘The current study deals with exact soliton solutions for Schrödinger-Hirota(SH)equation via two modi-fied integration methods.Those methods are known as the improved(G/G)-expansion method and the Kudryashov method.This model is a generalized version of the nonlinear Schrödinger(NLS)equation with higher order dispersion and cubic nonlinearity.It can be considered as a more accurate approximation than the NLS equation in explaining wave propagation in the ocean and optical fibers.A novel deriva-tive operator named as the conformable truncated M-fractional is used to study the above mentioned model.The obtained results can be used in describing the Schrödinger-Hirota equation in some better way.Moreover the obtained results are verified through symbolic computational software.Also,the ob-tained results show that the suggested approaches have broaden capacity to secure some new soliton type solutions for the fractional differential equations in an effective way.In the end,the results are also explained through their graphical representations.
