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Conservatory of Kaup-Kupershmidt Equation to the Concept of Fractional Derivative with and without Singular Kernel
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作者 Abdon ATANGANA emile franc doungmo goufo 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2018年第2期351-361,共11页
Making use of the traditional Caputo derivative and the newly introduced Caputo-Fabrizio deriva- tive with fractional order and no singular kernel, we extent the nonlinear Kaup-Kupershmidt to the span of fractional ca... Making use of the traditional Caputo derivative and the newly introduced Caputo-Fabrizio deriva- tive with fractional order and no singular kernel, we extent the nonlinear Kaup-Kupershmidt to the span of fractional calculus. In the analysis, different methods of fixed-point theorem together with the concept of piccard L-stability are used, allowing us to present the existence and uniqueness of the exact solution to models with both versions of derivatives. Finally, we present techniques to perform some numerical simulations for both non-linear models and graphical simulations are provided for values of the order α = 1.00; 0.90. Solutions are shown to behave similarly to the standard well-known traveling wave solution of Kaup-Kupershmidt equation. 展开更多
关键词 Kaup-Kupershmidt equation fractional derivative fixed-point theorem numerical simulations
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