A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method

Abstract

In this work, the time-fractional Navier–Stokes equation is discussed using a calculational method, which is called the Sumudu-generalized Laplace transform decomposition method (DGLTDM). The fractional derivatives are defined in the Caputo sense. The (DGLTDM) is a hybrid of the Sumudu-generalized Laplace transform and the decomposition method. Three examples of the time-fractional Navier–Stokes equation are studied to check the validity and demonstrate the effectiveness of the current method. The results show that the suggested method succeeds remarkably well in terms of proficiency and can be utilized to study more problems in the field of nonlinear fractional differential equations (FDEs).

On the Multi-Dimensional Sumudu-Generalized Laplace Decomposition Method and Generalized Pseudo-Parabolic Equations

“…The generalized Laplace transform was first proposed in [13] and subsequently applied to solve certain nonlinear dynamical models with non-integer order in [14]. The time-fractional Navier-Stokes equation was studied in [15] by using the double Sumudu-Generalized Laplace Transform Decomposition Method. The purpose of this study is to generalize the pseudo-parabolic and we discussed some theorems for the multi-Sumudu-generalized Laplace transform.…”