Journal ArticleDOI
Analytical study of exact traveling wave solutions for time-fractional nonlinear Schrödinger equations
TLDR
In this article, the modified Kudryashov method and the sine-Gordon expansion approach have been applied to retrieve a series of exact solutions for the previously mentioned Schrodinger equations.Abstract:
The present paper deals with the time-fractional unstable nonlinear Schrodinger equation and the time fractional modified unstable nonlinear Schrodinger equation in the conformable context. For this aim, the modified Kudryashov method and the sine–Gordon expansion approach have been applied to retrieve a series of exact solutions for the previously mentioned equations. The potential of the schemes in producing exact traveling wave solutions of nonlinear conformable time-fractional equations is demonstrated.read more
Citations
More filters
Journal ArticleDOI
On some novel optical wave solutions to the paraxial M-fractional nonlinear Schrödinger dynamical equation
Kalim U. Tariq,H. Zainab,Aly R. Seadawy,Muhammad Younis,Syed Tahir Raza Rizvi,Abd Allah A. Mousa +5 more
TL;DR: In this paper, the M-fractional paraxial nonlinear Schrodinger equation with Kerr media was solved using modified simple equation method and the auxiliary equation method, and a set of novel travelling wave solutions were observed such as bright, dark, periodic and optical solitons.
Journal ArticleDOI
Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations
TL;DR: In this article, the exact solutions of nonlinear water wave equations (NLWWEs) in oceans through the invariant subspace scheme (ISS) were derived, and the stability analysis for the NLWWE was investigated through the linear stability scheme.
Journal ArticleDOI
New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators
TL;DR: Some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators are proved.
Journal ArticleDOI
A nonlinear Schrödinger equation describing the polarization mode and its chirped optical solitons
Mostafa Eslami,K. Hosseini,Mashallah Matinfar,Mohammad Mirzazadeh,Mousa Ilie,J. F. Gómez-Aguilar +5 more
TL;DR: A nonlinear Schrodinger equation describing the polarization mode in an optical fiber which involves different physical terms such as quintic nonlinearity, self-steepening effect, and self-frequency shift is investigated in this article.
Journal ArticleDOI
Analysis of the local Drude model involving the generalized fractional derivative
Alberto Fleitas,J. F. Gomez-Aguilar,Juan E. Nápoles Valdés,José M. Rodríguez,José M. Sigarreta +4 more
TL;DR: In this article, a generalized fractional derivative has been used to study the classical Drude model, which describes the motion of the electrons in a metal in the presence of an external electric field.
References
More filters
Journal ArticleDOI
A new definition of fractional derivative
TL;DR: A new definition of fractional derivative and fractional integral is given and it is shown that it is the most natural definition, and the most fruitful one.
Journal ArticleDOI
On conformable fractional calculus
TL;DR: The basic concepts in this new simple interesting fractional calculus called conformable fractional derivative are set and the fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.
Journal ArticleDOI
One method for finding exact solutions of nonlinear differential equations
TL;DR: In this article, a method for finding exact solutions of nonlinear differential equations is considered and modifications of the method are discussed, showing that the method is one of the most effective approaches for solving nonlinear problems.
Journal ArticleDOI
Simplest equation method to look for exact solutions of nonlinear differential equations
TL;DR: In this paper, a new method is presented to look for exact solutions of nonlinear differential equations by using the general solutions of the simplest nonlinear equations and taking into consideration all possible singularities of equation studied.
Journal ArticleDOI
General conformable fractional derivative and its physical interpretation
Dazhi Zhao,Maokang Luo +1 more
TL;DR: In this paper, a general conformable fractional derivative (GCFD) is proposed to describe the physical world, which is generalized from the concept of CFD proposed by Khalil.