A review of operational matrices and spectral techniques for fractional calculus
AH Bhrawy, TM Taha, JAT Machado - Nonlinear Dynamics, 2015 - Springer
Recently, operational matrices were adapted for solving several kinds of fractional
differential equations (FDEs). The use of numerical techniques in conjunction with …
differential equations (FDEs). The use of numerical techniques in conjunction with …
A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations
In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …
method for multi-term time–space fractional differential equation with Dirichlet boundary …
A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
AH Bhrawy, MA Abdelkawy - Journal of Computational Physics, 2015 - Elsevier
A shifted Legendre collocation method in two consecutive steps is developed and analyzed
to numerically solve one-and two-dimensional time fractional Schrödinger equations …
to numerically solve one-and two-dimensional time fractional Schrödinger equations …
Short overview of early developments of the Hardy Cross type methods for computation of flow distribution in pipe networks
Hardy Cross originally proposed a method for analysis of flow in networks of conduits or
conductors in 1936. His method was the first really useful engineering method in the field of …
conductors in 1936. His method was the first really useful engineering method in the field of …
Fast iterative method with a second-order implicit difference scheme for time-space fractional convection–diffusion equation
In this paper we intend to establish fast numerical approaches to solve a class of initial-
boundary problem of time-space fractional convection–diffusion equations. We present a …
boundary problem of time-space fractional convection–diffusion equations. We present a …
A Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equations
AH Bhrawy - Numerical Algorithms, 2016 - Springer
This article adapts an operational matrix formulation of the collocation method for the one-
and two-dimensional nonlinear fractional sub-diffusion equations (FSDEs). In the proposed …
and two-dimensional nonlinear fractional sub-diffusion equations (FSDEs). In the proposed …
[HTML][HTML] A computational approach for solving time fractional differential equation via spline functions
A computational approach based on finite difference scheme and a redefined extended B-
spline functions is presented to study the approximate solution of time fractional advection …
spline functions is presented to study the approximate solution of time fractional advection …
A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives
M Dehghan, M Abbaszadeh - Engineering with Computers, 2017 - Springer
Our main aim in the current paper is to find a numerical plan for 2D Rayleigh–Stokes model
with fractional derivative on irregular domains such as circular, L-shaped and a unit square …
with fractional derivative on irregular domains such as circular, L-shaped and a unit square …
Jacobi spectral collocation approximation for multi-dimensional time-fractional Schrödinger equations
In the present paper, we construct the numerical solution for time fractional (1+ 1)-and (1+ 2)-
dimensional Schrödinger equations (TFSEs) subject to initial boundary. The solution is …
dimensional Schrödinger equations (TFSEs) subject to initial boundary. The solution is …
Numerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of line
MS Hashemi, D Baleanu - Journal of Computational Physics, 2016 - Elsevier
We propose a simple and accurate numerical scheme for solving the time fractional
telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate ϑ is …
telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate ϑ is …