Analysis of Time-Fractional $$\phi ^{4}$$-Equation with Singular and Non-Singular Kernels

Rahman, Fazlur; Ali, Amir; Saifullah, Sayed

doi:10.1007/s40819-021-01128-w

Cited by 25 publications

(8 citation statements)

References 38 publications

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“…This method is used here for the first to study the nonlinear evolution of solitary potential in nonextensive plasma. The modified double Laplace decomposition method has also extensively used to reduce the spatiotemporal solutions corresponds for the linear as well as nonlinear deferential equation [40][41][42][43][44] .…”

Section: Modified Double Laplace Decomposition Methods (Mdldm)mentioning

confidence: 99%

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Electron-acoustic solitary potential in nonextensive streaming plasma

Khan

Algahtani

Irfan

et al. 2022

Sci Rep

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The linear/nonlinear propagation characteristics of electron-acoustic (EA) solitons are examined in an electron-ion (EI) plasma that contains negative superthermal (dynamical) electrons as well as positively charged ions. By employing the magnetic hydrodynamic (MHD) equations and with the aid of the reductive perturbation technique, a Korteweg-de-Vries (KdV) equation is deduced. The latter admits soliton solution suffering from the superthermal electrons and the streaming flow. The utility of the modified double Laplace decomposition method (MDLDM) leads to approximate wave solutions associated with higher-order perturbation. By imposing finite perturbation on the stationary solution, and with the aid of MDLDM, we have deduced series solution for the electron-acoustic excitations. The latter admits instability and subsequent deformation of the wave profile and can’t be noticed in the KdV theory. Numerical analysis reveals that thermal correction due to superthermal electrons reduces the dimensionless phase speed $$(\bar{U}_{ph})$$ ( U ¯ ph ) for EA wave. Moreover, a random motion spread out the dynamical electron fluid and therefore, gives rise to $$\bar{U}_{ph}$$ U ¯ ph . A degree enhancement in temperature of superthermal (dynamical) electrons tappers of (increase) the wave steeping and the wave dispersion, enhancing (reducing) the pulse amplitude and the spatial extension of the EA solitons. Interestingly, the approximate wave solution suffers oscillation that grows in time. Our results are important for understanding the coherent EA excitation, associated with the streaming effect of electrons in the EI plasma being relevant to the earth’s magnetosphere, the ionosphere, the laboratory facilities, etc.

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Section: Modified Double Laplace Decomposition Methods (Mdldm)mentioning

confidence: 99%

“…( 39) as where G(S 1 ) and A 0 , A 1 , A 2 • • • • • • can be obtained by using Eqs. ( 36) and (37) as Using Equations ( 42) and (43) in Eq. ( 41) we get the the following solution…”

Section: Applications Of Mdldmmentioning

confidence: 99%

Electron-acoustic solitary potential in nonextensive streaming plasma

Khan

Algahtani

Irfan

et al. 2022

Sci Rep

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“…Ahmad et al used the CF operator to study the fractional-order Ambartsumian problem [23]. Rahman et al [24] studied the f 4 -model with the CF and AB operators. Other applications are listed in the literature [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

On new computations of the time-fractional nonlinear KdV-Burgers equation with exponential memory

Ganie,

Mofarreh,

Khan

2024

Phys. Scr.

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This paper examines the Korteweg-de Vries-Burgers (KdV-Burgers) equation with nonlocal operators using the exponential decay and Mittag-Leﬄer kernels. The Caputo-Fabrizio and Atangana-Baleanu operators are used in the natural transform decomposition method (NTDM). By coupling a decomposition technique with the natural transform methodology, the method provides an eﬀective analytical solution. When the fractional order is equal to unity, the proposed approach computes a series form solution that converges to the exact values. By comparing the approximate solution to the precise values, the eﬃcacy and trustworthiness of the proposed method are conﬁrmed. Graphs are also used to illustrate the series solution for a certain non-integer orders. Finally, a comparison of both operators outcome is examined using diagrams and numerical data. These graphs show how the approximated solution’s graph and the precise solution’s graph eventually converge as the non-integer order gets closer to 1. The outcomes demonstrate the method’s high degree of accuracy and its wide applicability to fractional nonlinear evolution equations. In order to further explain these concepts, simulations are run using a computationally packed software that helps interpret the implications of solutions. NTDM is considered the best analytical method for solving fractional-order phenomena, especially KdV-Burgers equations.

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“…Here we remark that fractional derivative has not a unique definition. There have been introduced various definitions by researchers including singular and non-singular operators (Rahman et al 2021). Recently in this connection, see more work as (Ahmad et al 2021c;Alqahtani et al 2021;Goufo 2022, 2023).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Mathematical Model of COVID-19 via Fractional-Order Piecewise Derivative

Shah

Sinan

Abdeljawad

et al. 2023

Chaos Theory and Applications

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In this research work, we investigate a dynamical systems under piecewise equations with fractional order derivative (FOD). The respective derivative is taken in piecewise to investigate the sudden or abrupt changes occurs in the dynamics of the proposed model. The respective model represent an infectious disease due to corona virus. We establish a detail analysis about sensitivity of the model. Further, we develop a numerical scheme to simulate the model against various fractional order. The concerned results are displayed graphically also.

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Analysis of Time-Fractional $$\phi ^{4}$$-Equation with Singular and Non-Singular Kernels

Cited by 25 publications

References 38 publications

Electron-acoustic solitary potential in nonextensive streaming plasma

Electron-acoustic solitary potential in nonextensive streaming plasma

On new computations of the time-fractional nonlinear KdV-Burgers equation with exponential memory

Analysis of Nonlinear Mathematical Model of COVID-19 via Fractional-Order Piecewise Derivative

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