Numerical algorithm for the variable-order Caputo fractional functional differential equation

DOI10.1007/s11071-016-2797-yzbMath1349.65505OpenAlexW2342455717WikidataQ115381719 ScholiaQ115381719MaRDI QIDQ345580

Mahmoud A. Zaky, Ali H. Bhrawy

Publication date: 2 December 2016

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-016-2797-y

zbMATH Keywords

collocation methodChebyshev polynomialsfunctional differential equationfractional pantograph equationvariable-order fractional differential equations

Mathematics Subject Classification ID

Trigonometric interpolation (42A15) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Cites Work

• Unnamed Item
• Unnamed Item
• Numerical analysis of a new space-time variable fractional order advection-dispersion equation
• A Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equations
• A review of operational matrices and spectral techniques for fractional calculus
• Second-order approximations for variable order fractional derivatives: algorithms and applications
• Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
• A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
• Fractional integration and differentiation of variable order: an overview
• Numerical techniques for the variable-order time fractional diffusion equation
• Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets
• The periodic solutions of the compound singular fractional differential system with delay
• Fractional functional differential equations with causal operators in Banach spaces
• A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations
• Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation
• On mean square displacement behaviors of anomalous diffusions with variable and random orders
• Theory of fractional functional differential equations
• Fractional functional differential inclusions with finite delay
• Design of variable and adaptive fractional order FIR differentiators
• Introduction to functional differential equations
• Numerical solution of the two-sided space-time fractional telegraph equation via Chebyshev tau approximation
• Theory and applications of partial functional differential equations
• Variable order and distributed order fractional operators
• Existence of solutions of a delay differential equation with nonlocal condition
• On the exponential stability in mean square of neutral stochastic functional differential equations
• Shifted fractional-order Jacobi orthogonal functions: application to a system of fractional differential equations
• Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method
• A numerical technique for variable fractional functional boundary value problems
• A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures
• A characteristic difference method for the variable-order fractional advection-diffusion equation
• A fast gradient projection method for a constrained fractional optimal control
• Hamilton’s principle with variable order fractional derivatives
• Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere
• Stability of neutral-type functional differential equations
• Existence of solutions of a semilinear functional-differential evolution nonlocal problem
• Mechanics with variable-order differential operators
• The variable viscoelasticity oscillator
• Integration and differentiation to a variable fractional order
• Asymptotic behaviour of functional-differential equations with proportional time delays
• Efficient Legendre spectral tau algorithm for solving the two-sided space–time Caputo fractional advection–dispersion equation
• A highly accurate collocation algorithm for 1 + 1 and 2 + 1 fractional percolation equations
• A variable order constitutive relation for viscoelasticity
• A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation

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