Solution of fractional order Schrödinger equation by using Aboodh transform homotopy perturbation method

Document Type : Regular research papers

Authors

1 Shri S'ad Vidya Mandal Institute Of Technology

2 Sardar Vallabhbhai National Institute of Technology

Abstract

This study presents an analytical approach for solving the fractional-order Schrödinger equation using the Aboodh Transform Homotopy Perturbation Method (ATHPM). The proposed method provides an approximate analytical solution, benchmarked against the exact solution to demonstrate its accuracy. Unlike conventional methods, Aboodh Transform Homotopy Perturbation Method (ATHPM) offers a computationally efficient technique without requiring linearization or small-parameter assumptions. The results validate the method’s effectiveness, showing excellent agreement with exact solutions. The study includes a comparative analysis, highlighting ATHPM’s advantages over existing techniques. Additionally, multiple figures illustrate the behavior of the obtained solutions, reinforcing the accuracy of the method. Several comparison tables showcase ATHPM’s performance against the exact solution. Furthermore, a detailed comparative study with the Modified Generalized Mittag-Leffler Function Method (MGMLFM) is provided, demonstrating the robustness and efficiency of the proposed method.
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.Keywords: Schrödinger equation, Time fractional Partial differential equation, Homotopy perturbation method, Aboodh transform.

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