Cubic nonlinear fractional Schrödinger equation with conformable derivative and its new travelling wave solutions
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This article is published in Journal of Applied Mathematics and Computational Mechanics.The article was published on 2021-06-01 and is currently open access. It has received 1 citations till now. The article focuses on the topics: Schrödinger equation & Conformable matrix.read more
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Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrödinger equations
TL;DR: In this paper , a class of generalized time-space fractional nonlinear Schrödinger equations arising in mathematical physics is studied. But the authors focus on a class and apply the bifurcation theory method to obtain the exact complex doubly periodic solutions, solitary wave solutions and rational function solutions.
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
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The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
TL;DR: The (G'/G)-expansion method is firstly proposed in this paper, where G = G(xi) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equations, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained when the parameters are taken as special values.
Journal ArticleDOI
Fractional Schrödinger equation.
TL;DR: The Hermiticity of the fractional Hamilton operator and the parity conservation law for fractional quantum mechanics are established and the energy spectra of a hydrogenlike atom and of a fractional oscillator in the semiclassical approximation are found.
Journal ArticleDOI
Fractional quantum mechanics and Lévy path integrals
TL;DR: In this article, a new extension of a fractality concept in quantum physics has been developed and path integrals over the Levy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integral approach.
Book
Fractional Quantum Mechanics
TL;DR: Fractional path integrals over the paths of the Levy flights are defined and it is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractal paths leads to fractional quantum mechanics and fractional statistical mechanics.