Shallow water wave models with and without singular kernel: existence, uniqueness, and similarities

DOI10.1155/2017/4609834zbMath1426.35223OpenAlexW2586827336WikidataQ59147558 ScholiaQ59147558MaRDI QIDQ1992767

Sunil Kumar, Emile Franc Doungmo Goufo

Publication date: 5 November 2018

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2017/4609834

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Fractional partial differential equations (35R11)

Related Items

Operational matrix for Atangana-Baleanu derivative based on Genocchi polynomials for solving FDEs, Similarities in a fifth-order evolution equation with and with no singular kernel, Solution of fractional telegraph equation with Riesz space-fractional derivative, Solution for fractional forced KdV equation using fractional natural decomposition method, On the fractal dynamics for higher order traveling waves, Design of a high-gain observer for the synchronization of chimera states in neurons coupled with fractional dynamics, Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo-Fabrizio fractional derivative, Dynamics of traveling waves of variable order hyperbolic Liouville equation: regulation and control, The fuzzy fractional SIQR model of computer virus propagation in wireless sensor network using Caputo Atangana-Baleanu derivatives, Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators, A collocation method for fractional diffusion equation in a long time with Chebyshev functions, A behavioral analysis of KdVB equation under the law of Mittag-Leffler function, Unnamed Item, Unnamed Item, A dynamical model of asymptomatic carrier zika virus with optimal control strategies, Notes on fuzzy fractional Sumudu transform

Uses Software

• GTEngine

Cites Work

• Unnamed Item
• A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations
• Stability and convergence analysis of a variable order replicator-mutator process in a moving medium
• Fractional modelling arising in unidirectional propagation of long waves in dispersive media
• A new analysis for the Keller-Segel model of fractional order
• On a fractional order Ebola epidemic model
• On the invalidity of Fourier series expansions of fractional order
• Mathematical modelling, simulation, and optimal control of the 2014 ebola outbreak in west africa
• Fractional calculus: quo vadimus? (where are we going?)
• Modeling extreme-event precursors with the fractional diffusion equation
• A biomathematical view on the fractional dynamics of cellulose degradation
• New analytical method for gas dynamics equation arising in shock fronts
• Scattering and inverse scattering for first order systems
• Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system
• Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications
• APPLICATION OF THE CAPUTO-FABRIZIO FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL TO KORTEWEG-DE VRIES-BURGERS EQUATION∗