Approximate Solutions of Third-Order Time Fractional Dispersive Equations with Singular and Nonsingular Kernel Derivatives

The natural transform decomposition method (NTDM) is an effective analytical method that combines the Adomian decomposition method (ADM) and the novel integral transformation known as the natural transform (NT). In this current study, we examined the time fractional third-order dispersive equation (TFTDE) investigated using an analytical method known as NTDM. Fractional derivative (FD) is referred to as a Caputo (C), Caputo-Fabrizio (CF), and Atangana-Baleanu derivative in the Caputo manner (ABC). The current framework accurately depicts how the results for various fractional orders behave. The concepts in the examples are shown with numerical results. Graphs and tables are used to compare the exact solution and the approximate solution.