Laplace Homotopy Analysis Method to Study Fractional Non-Linear SchrodingerEquations Under Non-Singular Kernel

Study Fractional Non-Linear Schrodinger Equations

Abstract

The Schrodinger equations have various applications in quantum mechanics and physical sci
ences as they describe a wide range of wave propagation phenomena including dust-acoustic, Langmuir, and
electromagnetic waves in plasma physics. In the present article, we employ the Laplace homotopy analysis
scheme to derive exact and approximate solutions for the fractional-order Schrodinger equations under the
Atangana-Balenu derivative in Caputo sense. By employing the proposed technique, we establish complex
nonlinear fractional-order models and evaluate the efficacy by conducting numerical experiments as an appli
cation. Throughout the furnished computations, we include a comparison between the approximate values and
their corresponding exact solutions and obtain some analysis of the absolute error. The effectiveness of pro
posed method is validated through numerical and graphical simulations, with results compared to established
techniques such as the homotopy perturbation transform method (HPTM) and the Elzaki Adomian decom
position method (EADM). The outcome obtained confirms that the suggested approach is an alternative,
straightforward, precise, and effective for solving both linear and nonlinear equations.