A Legendre collocation method for fractional integro-differential equations

DOI10.1177/1077546310395977zbMath1271.65157OpenAlexW2047450993MaRDI QIDQ2846409

Abbas Saadatmandi, Mehdi Dehghan

Publication date: 5 September 2013

Published in: Journal of Vibration and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1077546310395977

zbMATH Keywords

collocation methodintegro-differential equationsLegendre polynomialsfractional derivativeCaputo derivative

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Fractional derivatives and integrals (26A33)

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Cites Work

• Unnamed Item
• Solution of fractional integro-differential equations by using fractional differential transform method
• Solving fractional diffusion and wave equations by modified homotopy perturbation method
• Numerical studies for a multi-order fractional differential equation
• Homotopy analysis method for fractional IVPs
• The Hamilton formalism with fractional derivatives
• Numerical methods for fourth-order fractional integro-differential equations
• The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method
• Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions
• A new operational matrix for solving fractional-order differential equations
• Fractional generalized splines and signal processing
• Recent applications of fractional calculus to science and engineering
• Long memory processes and fractional integration in econometrics
• Solving systems of fractional differential equations using differential transform method
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Numerical solution of fractional integro-differential equations by collocation method
• Solving a system of nonlinear fractional differential equations using Adomian decomposition
• Algorithms for the fractional calculus: a selection of numerical methods
• Numerical solution of the one-dimensional wave equation with an integral condition
• Fractional Euler—Lagrange Equations of Motion in Fractional Space
• Heisenberg's Equations of Motion with Fractional Derivatives
• A Hamiltonian Formulation and a Direct Numerical Scheme for Fractional Optimal Control Problems
• Computation of two time-dependent coefficients in a parabolic partial differential equation subject to additional specifications
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method
• Hamilton–Jacobi formulation of systems within Caputo's fractional derivative