Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense

• Published in: Physica scripta Vol. 95; no. 7; pp. 75218 - 75238
• Main Authors: Al-Smadi, Mohammed, Abu Arqub, Omar, Momani, Shaher
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.07.2020
• Subjects: conformable fractional derivative; conformable residual power series method; fractional partial differential equation; quantum mechanics; Schrödinger model
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ab96e0

Mathematical modeling of fractional resonant Schrödinger equations is an extremely significant topic in the classical of quantum mechanics, chromodynamics, astronomy, and anomalous diffusion systems. Based on conformable residual power series, a novel effective analytical approach is considered to solve classes of nonlinear time-fractional resonant Schrödinger equation and nonlinear coupled fractional Schrödinger equations under conformable fractional derivatives. The solution methodology lies in generating an infinite conformable series solution with reliable wave pattern by minimizing the residual error functions. The main motivation for using this approach is high accuracy convergence and low computational cost compared to other existing methods. In this orientation, the competency and capacity of the proposed method are examined by implementing several numerical applications. From a numerical viewpoint, the obtained results indicate that the method is intelligent and has several features in feasibility, stability, and suitability for dealing with many fractional models emerging in physics and optics using the new conformable derivative.