Modeling attractors of chaotic dynamical systems with fractal-fractional operators
From MaRDI portal
Publication:2213634
DOI10.1016/j.chaos.2019.04.020zbMath1448.65268OpenAlexW2938708012WikidataQ128015277 ScholiaQ128015277MaRDI QIDQ2213634
Publication date: 2 December 2020
Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.chaos.2019.04.020
Complex behavior and chaotic systems of ordinary differential equations (34C28) Attractors of solutions to ordinary differential equations (34D45) Numerical chaos (65P20) Fractional ordinary differential equations (34A08) Numerical methods for functional-differential equations (65L03)
Related Items
The numerical treatment of fractal‐fractional 2D optimal control problems by Müntz–Legendre polynomials ⋮ An accurate numerical algorithm to investigate the solution of fractal-fractional partial differential equations ⋮ Analysis of dengue model with fractal-fractional Caputo-Fabrizio operator ⋮ CHAOTIC BEHAVIOR OF MODIFIED STRETCH–TWIST–FOLD FLOW UNDER FRACTAL-FRACTIONAL DERIVATIVES ⋮ Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense ⋮ Application of fractal fractional derivative of power law kernel \((^{FFP}_0D_x^{\alpha,\beta})\) to MHD viscous fluid flow between two plates ⋮ Modeling and analysis of the polluted lakes system with various fractional approaches ⋮ Role of fractal-fractional derivative on ferromagnetic fluid via fractal Laplace transform: a first problem via fractal-fractional differential operator ⋮ Numerical analysis of a new Volterra integro-differential equation involving fractal-fractional operators ⋮ Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets ⋮ Analysis of MHD generalized first problem of Stokes' in view of local and non-local fractal fractional differential operators ⋮ Applications of magnetohydrodynamic couple stress fluid flow between two parallel plates with three different kernels ⋮ Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis ⋮ On group of Lie symmetry analysis, explicit series solutions and conservation laws for the time-fractional (2 + 1)-dimensional Zakharov-Kuznetsov \((q,p,r)\) equation ⋮ Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators ⋮ Novel chaotic systems with fractional differential operators: numerical approaches ⋮ Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials ⋮ Predefined-time convergence in fractional-order systems ⋮ A novel finite difference-spectral method for fractal mobile/immobile transport model based on Caputo-Fabrizio derivative ⋮ Spectral entropy analysis and synchronization of a multi-stable fractional-order chaotic system using a novel neural network-based chattering-free sliding mode technique ⋮ Fractional order biological snap oscillator: analysis and control ⋮ Fractal derivative fractional grey Riccati model and its application ⋮ On the fractional model of Fokker-Planck equations with two different operator ⋮ PROPERTIES AND INTEGRAL INEQUALITIES INVOLVING WITH THE GENERALIZED s-TYPE PREINVEX MAPPINGS IN FRACTAL SPACE ⋮ Analysis of MHD Couette flow by fractal-fractional differential operators ⋮ Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator ⋮ Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel ⋮ On the Caputo-Fabrizio fractal fractional representation for the Lorenz chaotic system ⋮ Modelling chaotic dynamical attractor with fractal-fractional differential operators ⋮ Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense ⋮ Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo-Fabrizio fractional derivative ⋮ Barycentric-Legendre interpolation method for solving two-dimensional fractional cable equation in neuronal dynamics ⋮ Numerical simulation of the fractal-fractional reaction diffusion equations with general nonlinear ⋮ CHAOTIC BEHAVIOR OF BHALEKAR–GEJJI DYNAMICAL SYSTEM UNDER ATANGANA–BALEANU FRACTAL FRACTIONAL OPERATOR ⋮ ON ANALYSIS OF FRACTIONAL ORDER MATHEMATICAL MODEL OF HEPATITIS B USING ATANGANA–BALEANU CAPUTO (ABC) DERIVATIVE ⋮ A FRACTAL-FRACTIONAL 2019-NCOV MODEL OF MAJOR DISASTER FOR HUMAN LIFE ⋮ Switched dual compound-compound anti-synchronization of hyperchaotic dynamical systems ⋮ Analysis of Lie symmetry, explicit series solutions, and conservation laws for the nonlinear time-fractional Phi-four equation in two-dimensional space ⋮ Numerical approach for solving two dimensional fractal-fractional PDEs using peridynamic method ⋮ Tangent nonlinear equation in context of fractal fractional operators with nonsingular kernel ⋮ Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data ⋮ Chaos and multiple attractors in a fractal-fractional Shinriki's oscillator model ⋮ New coincidence point results for generalized graph-preserving multivalued mappings with applications ⋮ Mathematical modeling and analysis of fractional-order brushless DC motor ⋮ Investigation of complex behaviour of fractal fractional chaotic attractor with Mittag-Leffler Kernel ⋮ NUMERICAL SOLUTION OF NONLINEAR FRACTAL–FRACTIONAL DYNAMICAL MODEL OF INTERPERSONAL RELATIONSHIPS WITH POWER, EXPONENTIAL AND MITTAG-LEFFLER LAWS ⋮ A new numerical approach for the analysis of variable fractal and fractional order differential equations ⋮ A meshless technique based on the moving least squares shape functions for nonlinear fractal-fractional advection-diffusion equation ⋮ AN IMPROVEMENT OF THE POWER-MEAN INTEGRAL INEQUALITY IN THE FRAME OF FRACTAL SPACE AND CERTAIN RELATED MIDPOINT-TYPE INTEGRAL INEQUALITIES ⋮ A NUMERICAL SCHEME BASED ON TWO- AND THREE-STEP NEWTON INTERPOLATION POLYNOMIALS FOR FRACTAL–FRACTIONAL VARIABLE ORDERS CHAOTIC ATTRACTORS ⋮ An efficient operation matrix method for solving fractal-fractional differential equations with generalized Caputo-type fractional-fractal derivative ⋮ A new fractional study on the chaotic vibration and state-feedback control of a nonlinear suspension system ⋮ Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators ⋮ NUMERICAL ANALYSIS OF NEWLY DEVELOPED FRACTAL-FRACTIONAL MODEL OF CASSON FLUID WITH EXPONENTIAL MEMORY ⋮ A HIGH ORDER NUMERICAL SCHEME FOR FRACTAL-FRACTIONAL LASER SYSTEM WITH CHAOS STUDY ⋮ On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings ⋮ Numerical investigation of fractional-order cholera epidemic model with transmission dynamics via fractal-fractional operator technique ⋮ Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays ⋮ Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system ⋮ Study of time fractional proportional delayed multi‐pantograph system and integro‐differential equations ⋮ Numerical solution of the multiterm time‐fractional diffusion equation based on reproducing kernel theory ⋮ Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain ⋮ Novel applications of the magnetohydrodynamics couple stress fluid flows between two plates with fractal‐fractional derivatives ⋮ Space fractional-order modeling for the sintering process of metal fibers via lattice Boltzmann method ⋮ THE DYNAMICS OF HIV/AIDS MODEL WITH FRACTAL-FRACTIONAL CAPUTO DERIVATIVE ⋮ ON NUMERICAL AND THEORETICAL FINDINGS FOR FRACTAL-FRACTIONAL ORDER GENERALIZED DYNAMICAL SYSTEM ⋮ Transmission dynamics and sensitivity analysis of pine wilt disease with asymptomatic carriers via fractal-fractional differential operator of Mittag-Leffler kernel ⋮ \(\mathscr{ABC}\) fractional derivative for Varicella-Zoster virus using two-scale fractal dimension approach with vaccination ⋮ ON FRACTAL-FRACTIONAL WATERBORNE DISEASE MODEL: A STUDY ON THEORETICAL AND NUMERICAL ASPECTS OF SOLUTIONS VIA SIMULATIONS ⋮ Analysis of blood liquor model via nonlocal and singular constant proportional Caputo hybrid differential operator ⋮ SIMPSON-LIKE INEQUALITIES FOR TWICE DIFFERENTIABLE (s,P)-CONVEX MAPPINGS INVOLVING WITH AB-FRACTIONAL INTEGRALS AND THEIR APPLICATIONS ⋮ An analysis of a mathematical fractional model of hybrid viscous nanofluids and its application in heat and mass transfer ⋮ A Legendre spectral-finite difference method for Caputo-Fabrizio time-fractional distributed-order diffusion equation ⋮ Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator ⋮ A comparison study of bank data in fractional calculus ⋮ Fractal fractional derivative operator method on MCF-7 cell line dynamics ⋮ Mathematical modeling for adsorption process of dye removal nonlinear equation using power law and exponentially decaying kernels ⋮ TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation ⋮ Unnamed Item ⋮ A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations ⋮ Analysis and numerical simulation of fractional model of bank data with fractal-fractional Atangana-Baleanu derivative ⋮ Analysis of two avian influenza epidemic models involving fractal-fractional derivatives with power and Mittag-Leffler memories ⋮ Numerical solution of nonlinear 2D optimal control problems generated by Atangana-Riemann-Liouville fractal-fractional derivative ⋮ A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative ⋮ Respiration effect on plankton-oxygen dynamics in view of non-singular time fractional derivatives ⋮ Riemann-Liouville derivative over the space of integrable distributions ⋮ Non-local fractional calculus from different viewpoint generated by truncated \(M\)-derivative ⋮ Analysis of hepatitis B disease with fractal-fractional Caputo derivative using real data from Turkey ⋮ Fractal diffusion from a geometric Ricci flow ⋮ Master-slave synchronization for glucose-insulin metabolism of type-1 diabetic mellitus model based on new fractal-fractional order derivative ⋮ Solving fractal differential equations via fractal Laplace transforms ⋮ Dynamical complexity in a tritrophic food chain model with prey harvesting ⋮ Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model ⋮ New fractional modelling and control analysis of the circumscribed self-excited spherical strange attractor ⋮ NUMERICAL TREATMENT OF THE SPACE–TIME FRACTAL–FRACTIONAL MODEL OF NONLINEAR ADVECTION–DIFFUSION–REACTION EQUATION THROUGH THE BERNSTEIN POLYNOMIALS ⋮ ANALYSIS OF FRACTAL–FRACTIONAL MALARIA TRANSMISSION MODEL ⋮ THE NUMERICAL TREATMENT OF NONLINEAR FRACTAL–FRACTIONAL 2D EMDEN–FOWLER EQUATION UTILIZING 2D CHELYSHKOV POLYNOMIALS ⋮ ATANGANA–SEDA NUMERICAL SCHEME FOR LABYRINTH ATTRACTOR WITH NEW DIFFERENTIAL AND INTEGRAL OPERATORS ⋮ A discussion on a generalized Geraghty multi-valued mappings and applications ⋮ Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations ⋮ Fractal fractional operator method on HER2+ breast cancer dynamics
Cites Work
- Modeling of a mass-spring-damper system by fractional derivatives with and without a singular kernel
- Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm
- Localization of hidden Chua's attractors
- Anomalous diffusion modeling by fractal and fractional derivatives
- Fractional Liénard type model of a pipeline within the fractional derivative without singular kernel
- Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system
- A fractional order pine wilt disease model with Caputo-Fabrizio derivative
- A fractional model for the dynamics of TB virus
- A new fractional model for tuberculosis with relapse via Atangana-Baleanu derivative
- Atangana-Baleanu fractional approach to the solutions of Bagley-Torvik and Painlevé equations in Hilbert space
- Modeling chickenpox disease with fractional derivatives: from Caputo to Atangana-Baleanu
- Approximate solution of tuberculosis disease population dynamics model
- Modeling the transmission dynamics of Avian influenza with saturation and psychological effect
- Time-space fabric underlying anomalous diffusion
- A chaotic attractor from Chua's circuit
- YET ANOTHER CHAOTIC ATTRACTOR
- Fractional modeling of blood ethanol concentration system with real data application
- Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel
- GENERATING MULTISCROLL CHAOTIC ATTRACTORS: THEORIES, METHODS AND APPLICATIONS