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

Advances in Difference Equations

article

Hosseini, K.¹  Ilie, M.¹  Mirzazadeh, M.²  Baleanu, D.³ 

[1] Department of Mathematics, Rasht Branch, Islamic Azad University;Department of Engineering Sciences, Faculty of Technology and Engineering, University of Guilan;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University;Institute of Space Sciences

关键词: \((2 + 1)\) -dimensional mKdV equation;    Caputo–Fabrizio time-fractional derivative;    Homotopy analysis transform method;    Analytic approximation;    Fixed-point theorem;    Existence and uniqueness of the solution;   

DOI  :  10.1186/s13662-020-02789-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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$\psi (x,y, t;u)$ , 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.

【 授权许可】

CC BY