Numerical Simulation of Nonlinear Ecological Models with Nonlocal and Nonsingular Fractional Derivative
DOI10.1007/978-981-15-2286-4_10zbMath1476.65184OpenAlexW3006728863MaRDI QIDQ4992725
Publication date: 10 June 2021
Published in: Mathematical Modelling in Health, Social and Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-981-15-2286-4_10
numerical simulationecological modelAtangana-Baleanu derivativeHopf and Turing bifurcationtime-fractional reaction-diffusion
Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Developmental biology, pattern formation (92C15) Ecology (92D40) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Bifurcations in context of PDEs (35B32) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Pattern formations in context of PDEs (35B36)
Cites Work
- Unnamed Item
- Chaos in periodically forced Holling type IV predator-prey system with impulsive perturba\-tions
- Mathematical biology. Vol. 1: An introduction.
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- Space-time fractional diffusion equation using a derivative with nonsingular and regular kernel
- Integral spectral Tchebyshev approach for solving space Riemann-Liouville and Riesz fractional advection-dispersion problems
- Spatial complexity of a predator-prey model with Holling-type response
- A fractional epidemiological model for computer viruses pertaining to a new fractional derivative
- Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws
- Blind in a commutative world: simple illustrations with functions and chaotic attractors
- Fractional derivatives with no-index law property: application to chaos and statistics
- The role of power decay, exponential decay and Mittag-Leffler function's waiting time distribution: application of cancer spread
- Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana-Baleanu fractional operator
- Atangana-Baleanu fractional approach to the solutions of Bagley-Torvik and Painlevé equations in Hilbert space
- Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations
- Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense
- Analysis and numerical simulation of multicomponent system with Atangana-Baleanu fractional derivative
- Numerical patterns in system of integer and non-integer order derivatives
- Numerical patterns in reaction-diffusion system with the Caputo and Atangana-Baleanu fractional derivatives
- Chaotic behaviour in system of noninteger-order ordinary differential equations
- Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems
- Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
- New numerical approach for fractional differential equations
- Numerical approach to fractional blow-up equations with Atangana-Baleanu derivative in Riemann-Liouville sense
- A Legendre-Laguerre-Galerkin Method for Uniform Euler-Bernoulli Beam Equation
- Fully Legendre Spectral Galerkin Algorithm for Solving Linear One-Dimensional Telegraph Type Equation
- New Tchebyshev‐Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations
- Cycles, chaos, and noise in predator-prey dynamics