Weakness and Mittag-Leffler stability of solutions for time-fractional Keller-Segel models

DOI10.1515/ijnsns-2018-0035zbMath1461.35218OpenAlexW2888588726MaRDI QIDQ1627915

J. Manimaran, L. Shangerganesh, Amar Debbouche, Yong Zhou

Publication date: 3 December 2018

Published in: International Journal of Nonlinear Sciences and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ijnsns-2018-0035

zbMATH Keywords

weak solutionFaedo-Galerkin methodKeller-Segel modelfractional PDEMittag-Leffler stability

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11)

Related Items

Numerical simulation for generalized space-time fractional Klein-Gordon equations via Gegenbauer wavelet ⋮ Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy ⋮ Well‐posedness and blow‐up of the fractional Keller–Segel model on domains ⋮ Existence and uniqueness of mild solutions for a final value problem for nonlinear fractional diffusion systems ⋮ Retracted: New numerical method for ordinary differential equations: Newton polynomial ⋮ Initial value problem for fractional Volterra integro-differential equations with Caputo derivative ⋮ Blow-up solutions of a time-fractional diffusion equation with variable exponents ⋮ Existence, uniqueness and \(L^\infty\)-bound for weak solutions of a time fractional Keller-Segel system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a time fractional reaction diffusion equation
• Existence and uniqueness of solutions of degenerate chemotaxis system
• A priori estimates for solutions of boundary value problems for fractional-order equations
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• On the time-fractional Navier-Stokes equations
• Global existence and asymptotic behavior for a time fractional reaction-diffusion system
• Existence and regularity of solutions to time-fractional diffusion equations
• Weak solutions of the time-fractional Navier-Stokes equations and optimal control
• Initiation of slime mold aggregation viewed as an instability
• Exact solutions of the simplified Keller-Segel model
• Mittag-Leffler stability of fractional order nonlinear dynamic systems
• Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Hermite pseudospectral method for the time fractional diffusion equation with variable coefficients
• Weak solutions to non-homogeneous boundary value problems for time-fractional diffusion equations
• Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem
• Instability in a generalized multi-species Keller-Segel chemotaxis model
• A new fractional operator of variable order: application in the description of anomalous diffusion
• Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order
• Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant
• The solution of fractional order epidemic model by implicit Adams methods
• Positive steady states of reaction-diffusion-advection competition models in periodic environment
• THE SCALAR KELLER–SEGEL MODEL ON NETWORKS
• A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1)
• A class of time‐fractional reaction‐diffusion equation with nonlocal boundary condition
• Weak-renormalized solutions for three species competition model in ecology
• On a Two Species Chemotaxis Model with Slow Chemical Diffusion
• Fractional variational calculus in terms of Riesz fractional derivatives
• Basic Theory of Fractional Differential Equations