Modified fractional variational iteration method for solving the generalized time-space fractional Schrödinger...

Area of Science:

• Applied Mathematics
• Fractional Calculus
• Mathematical Physics

Background:

• The generalized time-space fractional Schrödinger equation (GFNLS) models various phenomena in quantum mechanics and optics.
• Traditional methods for solving fractional differential equations can be computationally intensive and may lack efficiency.
• Developing robust numerical techniques is crucial for analyzing complex fractional models.

Purpose of the Study:

• To modify the fractional variational iteration method (FVIM) for solving the GFNLS.
• To investigate the approximate solutions and iterative structure of the GFNLS using the modified FVIM.
• To compare the efficacy of the modified FVIM against established methods.

Main Methods:

• The study is based on He's variational iteration method.
• A modified fractional variational iteration method (FVIM) is proposed.
• Fractional derivatives are handled in the sense of Caputo.
• Symbolic computation is employed to derive and analyze solutions.

Main Results:

• The modified FVIM successfully constructs approximate solutions for the GFNLS.
• The iterative structure and approximate iterative series of the solutions are investigated.
• Numerical results demonstrate the method's power and reliability.

Conclusions:

• The modified fractional variational iteration method is a powerful, reliable, and effective technique for solving the GFNLS.
• It offers advantages over traditional methods like the homotopy analysis method (HAM), homotopy perturbation method (HPM), Adomian decomposition method (ADM), and variational iteration method (VIM).
• The method provides a robust framework for analyzing fractional Schrödinger equations.