On the fractional signals and systems
From MaRDI portal
Publication:612613
DOI10.1016/j.sigpro.2010.08.003zbMath1203.94041OpenAlexW1968270757MaRDI QIDQ612613
Juan J. Trujillo, Manuel D. Ortigueira, Igor Podlubny, Richard L. Magin
Publication date: 29 December 2010
Published in: Signal Processing (Search for Journal in Brave)
Full work available at URL: https://figshare.com/articles/journal_contribution/On_the_Fractional_Signals_and_Systems/10959374
Fractional derivatives and integrals (26A33) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)
Related Items (69)
A new approach to space fractional differential equations based on fractional order Euler polynomials ⋮ A modified quasi-boundary value method for a backward problem for the inhomogeneous time conformable fractional heat equation in a cylinder ⋮ Stabilising model predictive control for discrete-time fractional-order systems ⋮ Existence and numerical simulation of solutions for nonlinear fractional pantograph equations ⋮ The analytical interface coupling of arbitrary-order fractional nonlinear hyperbolic scalar conservation laws ⋮ Performance analysis and experimental validation of 2-DOF fractional-order controller for underactuated rotary inverted pendulum ⋮ The baseline wandering noise removal from ECG signal using forward–backward Riemann Liouville fractional integral-based empirical wavelet transform approach ⋮ New analytical technique for solving a system of nonlinear fractional partial differential equations ⋮ Hard-Spring Bistability and Effect of System Parameters in a Two-Degree-of-Freedom Vibration System with Damping Modeled by a Fractional Derivative ⋮ Hyers-Ulam stability for a coupled system of fractional differential equation with \(p\)-Laplacian operator having integral boundary conditions ⋮ On the existence of solutions of fractional integro-differential equations ⋮ Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions ⋮ Existence of solution for delay fractional differential equations ⋮ Fractional integro-differential calculus and its control-theoretical applications. I: Mathematical fundamentals and the problem of interpretation ⋮ On the solutions of a nonlinear fractional integro-differential equation of pantograph type ⋮ Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an analytical approach ⋮ Applications of contractive-like mapping principles to interval-valued fractional integro-differential equations ⋮ A method for the integer-order approximation of fractional-order systems ⋮ Existence and uniqueness results of impulsive fractional neutral pantograph integro differential equations with delay ⋮ Ulam–Hyers stability for second-order non-instantaneous impulsive fractional neutral stochastic differential equations ⋮ Chaotic dynamics of the fractional order Schnakenberg model and its control ⋮ Stability analysis of fractional-order neural networks with time-varying delay utilizing free-matrix-based integral inequalities ⋮ Controllability of coupled fractional integrodifferential equations ⋮ HE–ELZAKI METHOD FOR SPATIAL DIFFUSION OF BIOLOGICAL POPULATION ⋮ Small-signal fractional-order model of PN junction long-base diode ⋮ Weakly singular Volterra integral equation with combined logarithmic-power-law kernel: analytical and computational consideration ⋮ A new accurate method for solving fractional relaxation-oscillation with Hilfer derivatives ⋮ Well posedness of second-order non-instantaneous impulsive fractional neutral stochastic differential equations ⋮ A result on solvability of some fractional integro-differential equations in abstract spaces ⋮ Mathematical analysis and numerical simulation of chaotic noninteger order differential systems with Riemann‐Liouville derivative ⋮ Initial value problems for arbitrary order fractional differential equations with delay ⋮ From a generalised Helmholtz decomposition theorem to fractional Maxwell equations ⋮ Step-variable-order fractional viscoelastic-viscoinertial constitutive model and experimental verification of cemented backfill ⋮ Conditional optimization problems: fractional order case ⋮ Variable order fractional systems ⋮ Pinning synchronization of fractional and impulsive complex networks via event-triggered strategy ⋮ On the properties of some operators under the perspective of fractional system theory ⋮ Two Cases of Digraph Structures Corresponding to Minimal Positive Realisation of Fractional Continuous-Time Linear Systems of Commensurate Order ⋮ Numerical approach to the controllability of fractional order impulsive differential equations ⋮ Stabilization of a class of fractional-order nonautonomous systems using quadratic Lyapunov functions ⋮ Bifurcations and chaos in a discrete SI epidemic model with fractional order ⋮ Control of the Temperature of a Finite Diffusive Interface Medium Using the CRONE Controller ⋮ A new technique to solve the initial value problems for fractional fuzzy delay differential equations ⋮ Regularization and error estimates for an inverse heat problem under the conformable derivative ⋮ \(\Phi\)-Haar wavelet operational matrix method for fractional relaxation-oscillation equations containing \(\Phi\)-Caputo fractional derivative ⋮ NEIMARK BIFURCATIONS OF A GENERALIZED DUFFING–VAN DER POL OSCILLATOR WITH NONLINEAR FRACTIONAL ORDER DAMPING ⋮ Approximate limit cycles of coupled nonlinear oscillators with fractional derivatives ⋮ Stabilization of unstable equilibrium point of rotary inverted pendulum using fractional controller ⋮ Analytical solutions of fractional foam drainage equation by residual power series method ⋮ Fractional-order model of two-prey one-predator system ⋮ Signal processing for nondifferentiable data defined on Cantor sets: a local fractional Fourier series approach ⋮ Application of the collocation method for solving nonlinear fractional integro-differential equations ⋮ Solving interval-valued fractional initial value problems under Caputo gH-fractional differentiability ⋮ Minimal positive realizations of linear continuous-time fractional descriptor systems: two cases of an input-output digraph structure ⋮ On the numerical computation of the Mittag-Leffler function ⋮ A graphic stability criterion for non-commensurate fractional-order time-delay systems ⋮ Finite-dimensional control of linear discrete-time fractional-order systems ⋮ Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain ⋮ A numerical study of fractional relaxation-oscillation equations involving \(\psi \)-Caputo fractional derivative ⋮ High-order solvers for space-fractional differential equations with Riesz derivative ⋮ Topology identification of fractional-order complex dynamical networks based on auxiliary-system approach ⋮ Numerical controllability of fractional dynamical systems ⋮ The failure of certain fractional calculus operators in two physical models ⋮ Comparison of Fractional- and Integer-Order Filters in Filtration of Myoelectric Activity Acquired from Biceps Brachii ⋮ Unnamed Item ⋮ Taylor's formula involving generalized fractional derivatives ⋮ A computational algorithm for simulating fractional order relaxation-oscillation equation ⋮ Robust stability bounds of uncertain fractional-order systems ⋮ Numerical solution of the fractional relaxation-oscillation equation by using reproducing kernel Hilbert space method
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solving systems of fractional differential equations by homotopy-perturbation method
- On the relation between the fractional Brownian motion and the fractional derivatives
- Homotopy perturbation method for nonlinear partial differential equations of fractional order
- Adomian decomposition: a tool for solving a system of fractional differential equations
- Application of He's variational iteration method to Helmholtz equation
- A numerical scheme for the solution of multi-order fractional differential equations
- On systems of linear fractional differential equations with constant coefficients
- Fractional differential equations as alternative models to nonlinear differential equations
- \(\alpha\)-analytic solutions of some linear fractional differential equations with variable coefficients
- Riesz potential operators and inverses via fractional centred derivatives
- Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
- On the initial conditions in continuous-time fractional linear systems
- A new IIR-type digital fractional order differentiator
- Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements
- System initial conditions vs derivative initial conditions
- On the quadratic mapping \(z\rightarrow z^{2}-\mu \) for complex \(\mu \) and \(z\): the fractal structure of its set, and scaling
- Numerical approach to differential equations of fractional order
- Editorial: Fractional calculus applications in signals and systems
- A coherent approach to non-integer order derivatives
- A new least-squares approach to differintegration modeling
- An approximate method for numerical solution of fractional differential equations
- Fractional system identification for lead acid battery state of charge estimation
- A review of the decomposition method in applied mathematics
- The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
- Mathematical physiology
- Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Solving frontier problems of physics: the decomposition method
- Stability results for collocation methods for Volterra integral equations
- An algorithm for the numerical solution of differential equations of fractional order
- Numerical solution of fractional order differential equations by extrapolation
- Two direct Tustin discretization methods for fractional-order differentiator/integrator.
- Efficient solution of multi-term fractional differential equations using P(EC)\(^m\)E methods
- A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
- Comparing numerical methods for the solutions of systems of ordinary differential equations.
- Numerical solutions for systems of fractional differential equations by the decomposition method
- A predictor-corrector approach for the numerical solution of fractional differential equations
- Time fractional diffusion: A discrete random walk approach
- Numerical solution of the Bagley-Torvik equation.
- The Adomian method applied to some extraordinary differential equations
- Homotopy perturbation technique
- Solution of non-integer order differential equations via the Adomian decomposition method
- The fundamental solution of the space-time fractional advection-dispersion equation
- Approximate analytical solution to fractional modified KdV equations
- Numerical comparison of methods for solving linear differential equations of fractional order
- An efficient method for solving systems of fractional integro-differential equations
- Numerical solution of semidifferential equations by collocation method
- Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review
- Solving a system of nonlinear fractional differential equations using Adomian decomposition
- On Poisson's ratio in linearly viscoelastic solids
- An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method
- Solution of an extraordinary differential equation by Adomian decomposition method
- An explicit and numerical solutions of the fractional KdV equation
- Discretized Fractional Calculus
- On the Appearance of the Fractional Derivative in the Behavior of Real Materials
- Solving Ordinary Differential Equations I
- Linear approximation of transfer function with a pole of fractional power
- On the Stability of Linear Multistep Methods for Volterra Convolution Equations
- Two-dimensional differential transform method, Adomian's decomposition method, and variational iteration method for partial differential equations
- On a Concept of Derivative of Complex Order with Applications to Special Functions
- Fast Numerical Solution of Nonlinear Volterra Convolution Equations
- Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
- Generalized compound quadrature formulae for finite-part integrals
- Modal synthesis when modeling damping by use of fractional derivatives
- Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
- The time fractional diffusion equation and the advection-dispersion equation
- Differences of Fractional Order
- Optimal Fractional Controllers for Rational Order Systems: A Special Case of the Wiener-Hopf Spectral Factorization Method
- Advances in Fractional Calculus
- Discretization schemes for fractional-order differentiators and integrators
- On the Usefulness of Riemann-Liouville and Caputo Derivatives in Describing Fractional Shift-invariant Linear Systems
- Linear Differential Equations of Fractional Order
- Fractional Brownian Motions, Fractional Noises and Applications
- Definition of Physically Consistent Damping Laws with Fractional Derivatives
- An Approximate Solution for One-Dimensional Weakly Nonlinear Oscillations
- Analysis of fractional differential equations
This page was built for publication: On the fractional signals and systems
