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

Abstract

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.

Modified analytical approach for generalized quadratic and cubic logistic models with Caputo-Fabrizio fractional derivative

“…On the other hand, several concepts of fractional operators have been presented and developed in contrast to classic operators in calculus that have a clear concept and accurate engineering and physical interpretations. Among the well-known definitions widely employed in the context of fractional calculus are Riemann–Liouville, Caputo, Atangana–Baleanu, Riesz fractional operators [17] , [18] , [19] , [20] , [21] , [22] . Nevertheless, these definitions have several outstanding questions and some limitations.…”

Numerical simulation of telegraph and Cattaneo fractional‐type models using adaptive reproducing kernel framework

“…Several definitions and concepts have been introduced in the existing literature for the fractional derivatives, including Grünwald-Letnikov, Atangana-Balenau-Caputo, Caputo-Liouville, Caputo-Fabrizio, Hadamard, conformable, and many others. [38][39][40][41] For more convenience, this section briefly proposes some definitions, notations, and properties of the Caputo definition, which is central to the present investigation. For more details on fractional operators, we refer to other studies [42][43][44][45] and references therein.…”

On numerical approximation of Atangana-Baleanu-Caputo fractional integro-differential equations under uncertainty in Hilbert Space

“…On the other hand, the theory of fractional calculus is an interesting topic, not only among mathematicians but also among physicists and engineers for its great importance applications in many fields of engineering and sciences [11][12][13][14][15][16][17]. It has been investigated extensively for describing memory and hereditary for various physical and engineering applications similar to rheology, continuum mechanics, entropy, electromagnetic problems, thermodynamics and so forth [18][19][20][21][22][23][24][25].…”