New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burgers equations

DOI10.1007/s40314-018-0627-1zbMath1432.35229OpenAlexW2801412973WikidataQ129973254 ScholiaQ129973254MaRDI QIDQ1993507

Khaled M. Saad, Abdon Atangana, Dumitru Baleanu

Publication date: 5 November 2018

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-018-0627-1

zbMATH Keywords

Liouville-CaputoAtangana-BaleanuCaputo-Fabrizioq-homotopy analysis transform methodtime fractional Korteweg-de Vriestime fractional Korteweg-de Vries-Burgers

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
• A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations
• Analysis of the Keller-Segel model with a fractional derivative without singular kernel
• A new integral transform operator for solving the heat-diffusion problem
• Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm
• The time-fractional coupled-Korteweg-de-Vries equations
• Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order
• Comparing the Atangana-Baleanu and Caputo-Fabrizio derivative with fractional order: Allen Cahn model
• On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
• Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction-diffusion systems
• Traveling wave solutions to a reaction-diffusion equation
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• On the homotopy analysis method for nonlinear problems.
• On a hybrid spectral exponential Chebyshev method for time-fractional coupled Burgers equations on a semi-infinite domain
• Irving-Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel
• Modelling fractal waves on shallow water surfaces via local fractional Korteweg-de Vries equation
• New discretization of Caputo-Fabrizio derivative
• A new fractional operator of variable order: application in the description of anomalous diffusion
• Comparison between the homotopy analysis method and homotopy perturbation method
• On coupled systems of time-fractional differential problems by using a new fractional derivative
• A new method for exact solutions of variant types of time-fractional Korteweg-de Vries equations in shallow water waves
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• A new dissipation model based on memory mechanism
• Beyond Perturbation
• Travelling wave solutions and proper solutions to the two-dimensional Burgers–Korteweg–de Vries equation
• Exponential stability analysis of travelling waves solutions for nonlinear delayed cellular neural networks
• On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
• On the analysis of chemical kinetics system pertaining to a fractional derivative with Mittag-Leffler type kernel
• On travelling wave solutions of the Burgers–Korteweg–de Vries equation
• A new analysis for fractional model of regularized long‐wave equation arising in ion acoustic plasma waves
• A non-linear equation incorporating damping and dispersion

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