Series solutions for nonlinear time-fractional Schrödinger equations: Comparisons between conformable and Caputo derivatives

Oqielat, Moa’ath N.; El-Ajou, Ahmad; Al–Zhour, Zeyad; Alkhasawneh, Raed; Alrabaiah, Hussam

doi:10.1016/j.aej.2020.01.023

Cited by 47 publications

(15 citation statements)

References 39 publications

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“…Arbitrary -solutions play a dominant role in non-relativistic quantum mechanics since the wave function and associated eigenvalues contain all the necessary information for a full description of a quantum system [5][6][7][8]. With the experimental verification of the Schrödinger equation, researchers have devoted much interest in solving the radial Schrödinger equation to obtain bound state solutions with various methods for some potential models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020

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In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

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Section: Introductionmentioning

confidence: 99%

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020

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“…where ∇ N u, ∇ S u, ∇ E u, and ∇ W u are defined as in (37), (38), (39), and (40), respectively, and…”

Section: Numerical Methods Of the Proposed Modelmentioning

confidence: 99%

“…There are many definitions of fractional derivatives (three popular definitions were given by Grunwald-Letnikov (G-L), Riemann-Liouville (R-L), and Caputo). These have been used in numerous fields of science such as study of the anomalous diffusion phenomenon [24][25][26], circuit theory [27][28][29], and image processing [30,31], among other applications [11,[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Given the discussion above, we consider that using anisotropic diffusion models to eliminate noise in an image, preserving both strong and weak edges and without phenomena such as staircase, speckle, or any type of artifact, is a subject where much remains to be investigated.…”

Section: Introduction and Some Basic Definitionsmentioning

confidence: 99%

Perona-Malik Model with Diffusion Coefficient Depending on Fractional Gradient via Caputo-Fabrizio Derivative

Nchama¹,

Mecías²,

Ricard³

2020

Abstract and Applied Analysis

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The Perona-Malik (PM) model is used successfully in image processing to eliminate noise while preserving edges; however, this model has a major drawback: it tends to make the image look blocky. This work proposes to modify the PM model by introducing the Caputo-Fabrizio fractional gradient inside the diffusivity function. Experiments with natural images show that our model can suppress efficiently the blocky effect. Also, our model has good performance in visual quality, high peak signal-to-noise ratio (PSNR), and lower value of mean absolute error (MAE) and mean square error (MSE).

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“…In this section, a brief introduction to the definition and properties of the conformable fractional derivative will be given [11,12,[37][38][39][40].…”

Section: Preliminariesmentioning

confidence: 99%

Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative

Malik

Mohammed

2020

J Egypt Math Soc

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In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane-Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy-Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the solutions of the non-linear cases of the CL-M in terms of fractional convergent series in which its components can be computed in an easy manner. Finally, the results are given by graphs for each case of the CL-M at different values of α in order to demonstrate its accuracy, applicability, and efficiency.

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Series solutions for nonlinear time-fractional Schrödinger equations: Comparisons between conformable and Caputo derivatives

Cited by 47 publications

References 39 publications

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

Perona-Malik Model with Diffusion Coefficient Depending on Fractional Gradient via Caputo-Fabrizio Derivative

Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative

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