Finite difference scheme for time‐space fractional diffusion equation with fractional boundary conditions
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6132
Abstract: In this paper, the finite difference scheme is developed for the time‐space fractional diffusion equation with Dirichlet and fractional boundary conditions. The time and space fractional derivatives are considered in the senses of Caputo and… read more here.
Keywords: time space; space fractional; scheme; finite difference ... See more keywords
Efficient preconditioner of one-sided space fractional diffusion equation
Sign Up to like & getrecommendations! Published in 2018 at "BIT Numerical Mathematics"
DOI: 10.1007/s10543-018-0699-8
Abstract: In this paper, we propose an efficient preconditioner for the linear systems arising from the one-sided space fractional diffusion equation with variable coefficients. The shifted Gr$$\ddot{\mathrm{u}}$$u¨nwald formula is employed to discretize the one-sided Riemann–Liouville fractional… read more here.
Keywords: efficient preconditioner; fractional diffusion; one sided; sided space ... See more keywords
The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations
Sign Up to like & getrecommendations! Published in 2017 at "Numerical Algorithms"
DOI: 10.1007/s11075-017-0291-3
Abstract: An efficient local extrapolation of the exponential operator splitting scheme is introduced to solve the multi-dimensional space-fractional nonlinear Schrödinger equations. Stability of the scheme is examined by investigating its amplification factor and by plotting the… read more here.
Keywords: scheme; schr dinger; dinger equations; space fractional ... See more keywords
Differential quadrature method for space-fractional diffusion equations on 2D irregular domains
Sign Up to like & getrecommendations! Published in 2017 at "Numerical Algorithms"
DOI: 10.1007/s11075-017-0464-0
Abstract: In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by Lévy processes, which are sometimes called super-diffusion equations. In this article, we develop the differential quadrature… read more here.
Keywords: fractional diffusion; diffusion; space fractional; diffusion equations ... See more keywords
Numerical treatment of the space fractional advection–dispersion model arising in groundwater hydrology
Sign Up to like & getrecommendations! Published in 2021 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-020-01410-5
Abstract: This paper studies a new computational method for the approximate solution of the space fractional advection–dispersion equation in sense of Caputo derivatives. In the first method, a time discretization is accomplished via the compact finite… read more here.
Keywords: space fractional; advection dispersion; hydrology; fractional advection ... See more keywords
Solutions of 1-D Dispersive Equation with Time and Space-Fractional Derivatives
Sign Up to like & getrecommendations! Published in 2017 at "International Journal of Applied and Computational Mathematics"
DOI: 10.1007/s40819-017-0462-x
Abstract: This paper applied Adomian decomposition method to obtain the solution of fractional third-order dispersive equation with time and space-fractional derivatives. The iterative technique is carried out in a straightforward manner without the need for transforms… read more here.
Keywords: equation time; space fractional; dispersive equation; time space ... See more keywords
Numerical approximations for the Riesz space fractional advection-dispersion equations via radial basis functions
Sign Up to like & getrecommendations! Published in 2019 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2019.05.011
Abstract: Abstract The radial basis functions collocation method is developed to solve Riesz space fractional advection-dispersion equation (RSFADE). To do this, we first provide the Riemann-Liouville fractional derivatives of the five kinds of RBFs, including the… read more here.
Keywords: basis functions; fractional advection; space; riesz space ... See more keywords
Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2021.05.009
Abstract: Abstract We consider terminal value problems for time-space fractional pseudo-parabolic equation subjected to a final/terminal value condition. In fact, fractional orders α , s are not exactly known in modeling. These are determined experimentally. The… read more here.
Keywords: problems time; time; pseudo parabolic; fractional pseudo ... See more keywords
Space-fractional Euler-Bernoulli beam model - Theory and identification for silver nanobeam bending
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Mechanical Sciences"
DOI: 10.1016/j.ijmecsci.2020.105902
Abstract: Abstract This paper is concentrated on the non-local bending analysis of nanobeams and the improvement of the space-Fractional Euler-Bernoulli beam (s-FEBB) theory. A new kinematics is proposed for s-FEBB and a numerical algorithm is developed… read more here.
Keywords: space fractional; fractional euler; silver nanobeam; nanobeam bending ... See more keywords
Second-order BDF time approximation for Riesz space-fractional diffusion equations
Sign Up to like & getrecommendations! Published in 2018 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2017.1366461
Abstract: ABSTRACT Second-order backward difference formula (BDF2) is considered for time approximation of Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by the second-order fractional centre difference formula. To improve the computational efficiency, an… read more here.
Keywords: fractional diffusion; space; space fractional; second order ... See more keywords
2-D Modeling and Analysis of Time-Domain Electromagnetic Anomalous Diffusion With Space-Fractional Derivative
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Geoscience and Remote Sensing"
DOI: 10.1109/tgrs.2023.3241150
Abstract: Recently, the electromagnetic (EM) anomalous diffusion phenomenon has been observed in time-domain EM (TDEM) surveys. Furthermore, the data interpretation accuracy has been reduced by adopting the traditional EM theory and methods. A number of models,… read more here.
Keywords: diffusion; fractional derivative; space fractional; anomalous diffusion ... See more keywords