Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative

Ghanbari, Behzad

doi:10.1002/mma.7302

Cited by 129 publications

(12 citation statements)

References 43 publications

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“…In 2018, an integration method called the generalized exponential rational function method (GERFM) was introduced by Ghanbari et al to solve the resonance nonlinear Schrödinger equation [66]. Following their work, the technique has been used successfully many times to handle other partial equations [67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82]. In this part, we outline the main steps of GERFM as follows.…”

Section: The Generalized Exponential Rational Function Methodsmentioning

confidence: 99%

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Neirameh

Parvaneh

2021

Adv Differ Equ

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Exact solutions to nonlinear differential equations play an undeniable role in various branches of science. These solutions are often used as reliable tools in describing the various quantitative and qualitative features of nonlinear phenomena observed in many fields of mathematical physics and nonlinear sciences. In this paper, the generalized exponential rational function method and the extended sinh-Gordon equation expansion method are applied to obtain approximate analytical solutions to the space-time conformable coupled Cahn–Allen equation, the space-time conformable coupled Burgers equation, and the space-time conformable Fokas equation. Novel approximate exact solutions are obtained. The conformable derivative is considered to obtain the approximate analytical solutions under constraint conditions. Numerical simulations obtained by the proposed methods indicate that the approaches are very effective. Both techniques employed in this paper have the potential to be used in solving other models in mathematics and physics.

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Section: The Generalized Exponential Rational Function Methodsmentioning

confidence: 99%

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Neirameh

Parvaneh

2021

Adv Differ Equ

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“…In the past few decades, various advanced computational approaches, e.g., finite element, numerical linear algebra, statistics, numerical analysis, tensor analysis, and artificial intelligence, have been applied in various fields of study, such as fluid mechanic engineering [26][27][28][29][30][31][32][33][34], chemical engineering [35][36][37][38][39][40][41], electrical and computer engineering , petrochemical engineering [73][74][75][76][77], petroleum engineering [78][79][80][81][82][83][84][85][86][87][88][89][90][91][92], mathematics and physics [93][94][95][96][97][98][99][100][101][102], and environmental engineering [103]…”

Section: Mlp Neural Networkmentioning

confidence: 99%

Application of Neural Network and Time-Domain Feature Extraction Techniques for Determining Volumetric Percentages and the Type of Two Phase Flow Regimes Independent of Scale Layer Thickness

et al. 2022

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One of the factors that significantly affects the efficiency of oil and gas industry equipment is the scales formed in the pipelines. In this innovative, non-invasive system, the inclusion of a dual-energy gamma source and two sodium iodide detectors was investigated with the help of artificial intelligence to determine the flow pattern and volume percentage in a two-phase flow by considering the thickness of the scale in the tested pipeline. In the proposed structure, a dual-energy gamma source consisting of barium-133 and cesium-137 isotopes emit photons, one detector recorded transmitted photons and a second detector recorded the scattered photons. After simulating the mentioned structure using Monte Carlo N-Particle (MCNP) code, time characteristics named 4th order moment, kurtosis and skewness were extracted from the recorded data of both the transmission detector (TD) and scattering detector (SD). These characteristics were considered as inputs of the multilayer perceptron (MLP) neural network. Two neural networks that were able to determine volume percentages with high accuracy, as well as classify all flow regimes correctly, were trained.

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“…e time-fractional SDE has been investigated through various methods, such as the homotopy perturbation method [35], exponential rational function method [36], residual power series method [37], modified transformation method [38], two-dimensional differential transform method [39], extended simple equation method [40], trigonometric B-spline method [41], fractional reduced differential transform method [42], and homotopy analysis method [43]. All these methods have their own specific limits and deficiencies.…”

Section: Id ]mentioning

confidence: 99%

A Highly Accurate Technique to Obtain Exact Solutions to Time‐Fractional Quantum Mechanics Problems with Zero and Nonzero Trapping Potential

Liaqat

Khan

Alam

et al. 2022

Journal of Mathematics

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In this study, the highly accurate analytical Aboodh transform decomposition method (ATDM) in the sense of Caputo fractional derivative is used to determine the approximate and exact solutions of both linear and nonlinear time-fractional Schrodinger differential equations (SDEs) with zero and nonzero trapping potential that describe the nonrelativistic quantum mechanical activity. The Adomian decomposition method (ADM) and the Aboodh transform of Caputo’s fractional derivative are combined in this method. The recurrence and absolute error of the four problems are analyzed to evaluate the efficiency and consistency of the presented method. In addition, numerical results are also compared with other methods such as the fractional reduced differential transform method (FRDTM), the homotopy analysis method (HAM), and the homotopy perturbation method (HPM). The results obtained by the proposed method show excellent agreement with these methods, which indicates its effectiveness and reliability. This technique has the benefit of not requiring any minor or major physical parameter assumptions in the problem. As a result, it may be used to solve both weakly and strongly nonlinear problems, overcoming some of the inherent constraints of classic perturbation approaches. To solve nonlinear fractional-order differential equations, just a few computations are necessary. As a consequence, it outperforms homotopy analysis and homotopy perturbation approaches significantly. The procedure is quick, precise, and easy to implement. Convergence analysis of the series solution is also offered.

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Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative

Cited by 129 publications

References 43 publications

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Application of Neural Network and Time-Domain Feature Extraction Techniques for Determining Volumetric Percentages and the Type of Two Phase Flow Regimes Independent of Scale Layer Thickness

A Highly Accurate Technique to Obtain Exact Solutions to Time‐Fractional Quantum Mechanics Problems with Zero and Nonzero Trapping Potential

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