Bernstein polynomials for solving fractional heat- and wave-like equations

DOI10.2478/S13540-012-0039-7zbMath1312.65168OpenAlexW2079974799MaRDI QIDQ2347194

Kobra Karimi, Davood Rostamy

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-012-0039-7

zbMATH Keywords

Bernstein polynomialsoperational matrixfractional heat- and wave-like equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Approximation by polynomials (41A10) Approximation by other special function classes (41A30) Fractional partial differential equations (35R11)

Related Items (15)

New local discontinuous Galerkin method for a fractional time diffusion wave equation ⋮ Chaotic behaviour of fractional predator-prey dynamical system ⋮ An efficient method for the analytical study of linear and nonlinear time-fractional partial differential equations with variable coefficients ⋮ Bivariate discrete Mittag-Leffler functions with associated discrete fractional operators ⋮ Identifying an unknown time-dependent boundary source in time-fractional diffusion equation with a non-local boundary condition ⋮ A convergent algorithm for solving higher-order nonlinear fractional boundary value problems ⋮ Approximate analytical solution for nonlinear system of fractional differential equations by BPS operational matrices ⋮ Normalized Bernstein polynomials in solving space-time fractional diffusion equation ⋮ Approximate solution for system of fractional non-linear dynamical marriage model using Bernstein polynomials ⋮ Discrete Mittag-Leffler kernel type fractional difference initial value problems and Gronwall's inequality ⋮ Exponential Bernstein functions: an effective tool for the solution of heat transfer of a micropolar fluid through a porous medium with radiation ⋮ Analytical analysis of fractional-order physical models via a Caputo-Fabrizio operator ⋮ The arbitrary-order fractional hyperbolic nonlinear scalar conservation law ⋮ Unnamed Item ⋮ A note on fractional Bessel equation and its asymptotics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
• Recent history of fractional calculus
• Implicit difference approximation for the time fractional diffusion equation
• Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
• The Adomian decomposition method for solving partial differential equations of fractal order in finite domains
• A new operational matrix for solving fractional-order differential equations
• Variational iteration method for fractional heat- and wave-like equations
• Algorithms for polynomials in Bernstein form
• Legendre-Bernstein basis transformations
• Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method
• An approximate solution for a fractional diffusion-wave equation using the decomposition method
• Numerical solution of electrodynamic flow by using pseudo-spectral collocation method
• Fractional-order dynamical models of love
• An explicit and numerical solutions of the fractional KdV equation
• Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder
• Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices
• Operational matrices of Bernstein polynomials and their applications

This page was built for publication: Bernstein polynomials for solving fractional heat- and wave-like equations