The role of fractional calculus in modeling biological phenomena: a review

From MaRDI portal

Publication:2007409

Jump to:navigation, search

DOI10.1016/j.cnsns.2017.04.001zbMath1467.92050OpenAlexW2606385482WikidataQ112880640 ScholiaQ112880640MaRDI QIDQ2007409

Publication date: 14 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2017.04.001

zbMATH Keywords

diffusion fractional calculus power-law biomedicine fractional order impedance impedance models respiratory impedance

Mathematics Subject Classification ID

Biomechanics (92C10) Physiology (general) (92C30)

Related Items

NONEXISTENCE RESULTS FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL INEQUALITIES INVOLVING ERDÉLYI–KOBER FRACTIONAL DERIVATIVES, Recovering source term and temperature distribution for nonlocal heat equation, Modelling radiation cancer treatment with a death-rate term in ordinary and fractional differential equations, Green's functions on various time scales for the time-fractional reaction-diffusion equation, Synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights and discontinuous nodes based on sliding mode control strategy, On solutions of linear and nonlinear fractional differential equations with application to fractional order RC type circuits, Dynamical analysis of a fractional discrete-time vocal system, On the Caputo fractional random boundary value problem, An efficient and robust numerical solver for impulsive control of fractional chaotic systems, Theoretical and numerical analysis of a prey-predator model (3-species) in the frame of generalized Mittag-Leffler law, Optimal approximation of analog PID controllers of complex fractional-order, A new numerical study of space–time fractional advection–reaction–diffusion equation with Rabotnov fractional‐exponential kernel, Fractional model of brain tumor with chemo-radiotherapy treatment, Spectral treatment for the fractional-order wave equation using shifted Chebyshev orthogonal polynomials, Exponential stability for an opinion formation model with a leader associated with fractional differential equations, Numerical study of distributed-order Bessel fractional derivative with application to Euler-Poisson-Darboux equation, $L2-1_\sigma$ Finite Element Method for Time-Fractional Diffusion Problems with Discontinuous Coefficients, Existence and stability for a nonlinear hybrid differential equation of fractional order via regular Mittag–Leffler kernel, Effects of global warming, time delay and chaos control on the dynamics of a chaotic atmospheric propagation model within the frame of Caputo fractional operator, Invariant subspace method and exact solutions of the coupled system of time-fractional convection-reaction-diffusion equations, The non-uniform L1-type scheme coupling the finite volume method for the time-space fractional diffusion equation with variable coefficients, Nonoscillatory solutions of discrete fractional order equations with positive and negative terms, High‐order schemes and their error analysis for generalized variable coefficients fractional reaction–diffusion equations, On some inequalities involving the function and its fractional derivative, Fractional type multivariate neural network operators, A positivity-preserving and robust fast solver for time-fractional convection-diffusion problems, On backward fractional pseudo parabolic equation: regularization by quasi-boundary value method, convergence rates, New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems, Unnamed Item, Unnamed Item, A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator, Immune response in HIV epidemics for distinct transmission rates and for saturated CTL response, Inverse problems for a multi-term time fractional evolution equation with an involution, Numerical solutions for fractional optimal control problems by using generalised fractional-order Chebyshev wavelets, A Study on Functional Fractional Integro-Differential Equations of Hammerstein type, Error estimates for Galerkin finite element approximations of time-fractional nonlocal diffusion equation, Parametric resonance of fractional multiple-degree-of-freedom damped beam systems, Numerical simulation for fractional-order differential system of a glioblastoma multiforme and immune system, The many facets of the Estrada indices of graphs and networks, Numerical approximations on the transient analysis of bioelectric phenomena at long time scales via the Mittag-Leffler function, Invariant subspace method for \((m+1)\)-dimensional non-linear time-fractional partial differential equations, Fractional Ornstein-Uhlenbeck noise, The extension of analytic solutions to FDEs to the negative half-line, A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations, Fractional driven-damped oscillator and its general closed form exact solution, Multivariate neural network interpolation operators, A spectral framework for fractional variational problems based on fractional Jacobi functions, Numerical simulation of a degenerate parabolic problem occurring in the spatial diffusion of biological population, Nonlinear fractional dynamics with kicks, Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems, Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media, Modelling and parameter identification for a two-stage fractional dynamical system in microbial batch process, Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems, Fractional order turbidostat model with the discrete delay of digestion, Fractional order models for viscoelasticity in lung tissues with power, exponential and Mittag-Leffler memories, Some new generalized result of Gronwall-Bellman-Bihari type inequality with some singularity, A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative, A simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion, Identification for control of suspended objects in non-Newtonian fluids, A fractional dynamical model for honeybee colony population, Generalized fractional controller for singular systems of differential equations, Time fractional cable equation and applications in neurophysiology, An innovative fractional order LMS algorithm for power signal parameter estimation, Can fractional calculus help improve tumor growth models?, Consensus of fractional-order multi-agent systems via current and time-delay states feedback, PREDICTIVE CONTROL OF THE VARIABLE-ORDER FRACTIONAL CHAOTIC ECOLOGICAL SYSTEM, Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives, Unnamed Item, Numerical schemes for a class of tempered fractional integro-differential equations, A new accurate method for solving fractional relaxation-oscillation with Hilfer derivatives, Optimal control of a fractional smoking system, New observations on optimal cancer treatments for a fractional tumor growth model with and without singular kernel, Decay Estimates in Time for Classical and Anomalous Diffusion, Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems, Comparative analysis of properties of weakening buffer operators in time series prediction models, Ulam-Hyers stability of Caputo-type fractional fuzzy stochastic differential equations with delay, Pinning synchronization of fractional and impulsive complex networks via event-triggered strategy, An anomalous diffusion model based on a new general fractional operator with the Mittag-Leffler function of Wiman type, An integro quadratic spline-based scheme for solving nonlinear fractional stochastic differential equations with constant time delay, Fractal-fractional modelling of partially penetrating wells, On fractional-order discrete-time systems: chaos, stabilization and synchronization, Asymptotical stability and asymptotic periodicity for the Lasota-Wazewska model of fractional order with infinite delays, Optimal stabilization and time step constraints for the forward Euler-local discontinuous Galerkin method applied to fractional diffusion equations, Modeling the dependence of barometric pressure with altitude using Caputo and Caputo-Fabrizio fractional derivatives, Time-fractional equations with reaction terms: fundamental solutions and asymptotics, Dynamical behaviors of Bazykin-Berezovskaya model with fractional-order and its discretization, Productivity with fatigue and long memory: fractional calculus approach, A note on the continuity in the hurst index of the solution of rough differential equations driven by a fractional brownian motion, A Mittag-Leffler fractional-order difference observer, On group analysis, conservation laws and exact solutions of time-fractional Kudryashov-Sinelshchikov equation, An efficient explicit decoupled group method for solving two-dimensional fractional Burgers' equation and its convergence analysis, Unnamed Item, New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian, Fractional order tube model reference adaptive control for a class of fractional order linear systems, A fractional-order compartmental model for the spread of the COVID-19 pandemic, Fractional Linear Systems with Memory Deficiency and Their State-Space Integer-Order Approximation, Fast second-order implicit difference schemes for time distributed-order and Riesz space fractional diffusion-wave equations, Generalized exponential time differencing schemes for stiff fractional systems with nonsmooth source term, Fractional-order closed-loop model reference adaptive control for anesthesia, On the recovery of a time dependent diffusion coefficient for a space fractional diffusion equation, Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics, An efficient localized collocation solver for anomalous diffusion on surfaces, A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains, An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy, Fractional type multivariate sampling operators, SIMULTANEOUS DETERMINATION OF A SOURCE TERM AND DIFFUSION CONCENTRATION FOR A MULTI-TERM SPACE-TIME FRACTIONAL DIFFUSION EQUATION, On numerical approximations of fractional-order spiking neuron models, From fractional differential equations with Hilfer derivatives. To discrete maps with memory, Initial value problem for the \((2+1)\)-dimensional time-fractional generalized convection-reaction-diffusion wave equation: invariant subspaces and exact solutions, Two energy-preserving numerical models for a multi-fractional extension of the Klein-Gordon-Zakharov system, Inverse source problems for a space–time fractional differential equation, Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids, On representation and interpretation of fractional calculus and fractional order systems, Unnamed Item, Cubature Kalman filters for nonlinear continuous-time fractional-order systems with uncorrelated and correlated noises, Comparison of dynamical behavior between fractional order delayed and discrete conformable fractional order tumor-immune system, An inverse source problem for anomalous diffusion equation with generalized fractional derivative in time, Caputo and related fractional derivatives in singular systems, On the existence of traveling fronts in the fractional-order amari neural field model, On the equivalence between fractional and classical oscillators, Bifurcation in a New Fractional Model of Cerebral Aneurysm at the Circle of Willis, Mixed logical dynamical modeling of discrete-time hybrid fractional systems, Numerical investigation of the variable-order fractional Sobolev equation with non-singular Mittag-Leffler kernel by finite difference and local discontinuous Galerkin methods, Deterministic coherence resonance analysis of coupled chaotic oscillators: fractional approach, Fault-tolerant adaptive fractional controller design for incommensurate fractional-order nonlinear dynamic systems subject to input and output restrictions, Stability of a time fractional advection-diffusion system, The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations, Tempered fractional LES modeling, A new efficient algorithm based on feedforward neural network for solving differential equations of fractional order, Asymptotic cycles in fractional maps of arbitrary positive orders, A new representation for the solutions of fractional differential equations with variable coefficients, ON THE NONLINEAR GENERALIZED LANGEVIN EQUATION INVOLVING ψ-CAPUTO FRACTIONAL DERIVATIVES, Analytical method on stabilisation of fractional-order plants with interval uncertainties using fractional-order PI^λ D^μ controllers, Mathematical Modeling for Asthma due to Air Pollution, Fractional-order Bessel wavelet functions for solving variable order fractional optimal control problems with estimation error

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:2007409&oldid=14478431"