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• W3207839478 abstract "In this article, we study the time-fractional nonlinear Klein–Gordon equation in Caputo–Fabrizio’s sense and Atangana–Baleanu–Caputo’s sense. The modified double Laplace transform decomposition method is used to attain solutions in the form of series of the proposed model under aforesaid fractional operators. The suggested method is the composition of the double Laplace transform and decomposition method. The convergence of the considered method is demonstrated for the considered model. It is observed that the obtained solutions converge to the exact solution of the proposed model. For validity, we consider two particular examples with appropriate initial conditions and derived the series solution in the sense of both operators for the considered model. From numerical solutions, it is observed that the considered model admits pulse-shaped solitons. It is also observed that the wave amplitude enhances with variations in time, which infers the coefficient <math xmlns=http://www.w3.org/1998/Math/MathML id=M1> <mi>α</mi> </math> significantly increases the wave amplitude and affects the nonlinearity/dispersion effects, therefore may admit monotonic shocks. The physical behavior of the considered numerical examples is illustrated explicitly which reveals the evolution of localized shock excitations." @default.
• W3207839478 created "2021-10-25" @default.
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• W3207839478 date "2021-10-13" @default.
• W3207839478 modified "2023-10-14" @default.
• W3207839478 title "Time-Fractional Klein–Gordon Equation with Solitary/Shock Waves Solutions" @default.
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• W3207839478 doi "https://doi.org/10.1155/2021/6858592" @default.
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