Baleanu, DumitruHosseini, K.Ilie, M.Mirzazade, M.Baleanu, Dumitru2020-12-312020-12-312020Hosseini, K...et al. (2020). "A detailed study on a new (2+1)-dimensional mKdV equation involving the Caputo-Fabrizio time-fractional derivative", Advances in Difference Equations, Vol. 2020, No. 1.1687-1847https://hdl.handle.net/20.500.12416/4421The 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.eninfo:eu-repo/semantics/openAccess(2 + 1)-Dimensional Mkdv EquationCaputo–Fabrizio Time-Fractional DerivativeHomotopy Analysis Transform MethodAnalytic ApproximationFixed-Point TheoremExistence and Uniqueness of the SolutionArticle2020110.1186/s13662-020-02789-5