A Fixed Point Theorem for Time-Fractional Fornberg-Whitham Equation Arising in Atmospheric Science (Contemporary Mathematics, 2024)
In this paper, we apply the Homotopy perturbation transform method of the time-fractional Fornberg-Whitham equation with Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness solutions of the time-fractional Fornberg-Whitham equation using fixed point theory. The physical interpretation of the nonlinear models are also discussed through the semi analytical solutions, which demonstrate the effectiveness of the proposed method. Finally, 2D and 3D graphs of some derived solutions are depicted through suitable parameter values.
Keywords: the time-fractional fornberg-whitham equation, fractional homotopy perturbation transform method (FHPTM), caputo fabrizio derivative (CFD), stability analysis, fixed point, laplace transform