A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo–Fabrizio time-fractional derivative

The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo–Fabrizio (CF) derivative. More explicitly, a new ( 2 + 1 ) -dimensional mKdV (2D-mKdV) equation involving the Caputo–Fabrizio time-fractional derivative is considered and an analytic a...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 13
Main Authors Hosseini, K., Ilie, M., Mirzazadeh, M., Baleanu, D.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 06.07.2020
Springer Nature B.V
SpringerOpen
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Summary:The present article aims to present a comprehensive study on a nonlinear time-fractional model involving the Caputo–Fabrizio (CF) derivative. More explicitly, a new ( 2 + 1 ) -dimensional mKdV (2D-mKdV) equation involving the Caputo–Fabrizio time-fractional derivative is considered and an analytic approximation for it is retrieved through a systematic technique, called the homotopy analysis transform (HAT) method. Furthermore, after proving the Lipschitz condition for the kernel ψ ( x , y , t ; u ) , the fixed-point theorem is formally utilized to demonstrate the existence and uniqueness of the solution of the new 2D-mKdV equation involving the CF time-fractional derivative. A detailed study finally is carried out to examine the effect of the Caputo–Fabrizio operator on the dynamics of the obtained analytic approximation.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02789-5