31 citations · 85 across the 10 of their papers we have counts for
10 papers
Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations
A. Yousefi, S. Javadi, E. Babolian +1
In this paper, we propose and analyze a spectral Chebyshev-Legendre approximation for fractional order integro-differential equations of Fredholm type. The fractional derivative is…
A Fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives
Salman Jahanshahi, Esmail Babolian, Delfim F. M. Torres +1
We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The prop…
Bernstein modal basis: application to the spectral Petrov-Galerkin method for fractional partial differential equations
Mostafa Jani, Esmail Babolian, Shahnam Javadi
In the spectral Petrov-Galerkin methods, the trial and test functions are required to satisfy particular boundary conditions. By a suitable linear combination of orthogonal polynom…
Bernstein dual-Petrov-Galerkin method: application to 2D time fractional diffusion equation
Mostafa Jani, Shahnam Javadi, Esmail Babolian +1
In this paper, we develop a Bernstein dual-Petrov-Galerkin method for the numerical simulation of a two-dimensional fractional diffusion equation. A spectral discretization is appl…
A numerical scheme for space-time fractional advection-dispersion equation
S. Javadi, M. Jani, E. Babolian
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and impleme…
Banded operational matrices for Bernstein polynomials and application to the fractional advection-dispersion equation
M. Jani, E. Babolian, S. Javadi +1
In the papers dealing with derivation and applications of operational matrices of Bernstein polynomials, a basis transformation, commonly a transformation to power basis, is used.…
Solving Abel integral equations of first kind via fractional calculus
Salman Jahanshahi, Esmail Babolian, Delfim F. M. Torres +1
We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional int…
Padé approximation
Hamed Mohebalizadeh, Esmail Babolian
To generalize the concept of Padé approximation for functions to more than one variable, several definitions have been introduced. All definitions have advantages and disadvantages…
A New Fast Numerical Method for One-Dimensional Nonlinear Sine-Gordon Equation Using Multivariate Padé approximation
Hamed Mohebalizadeh, Esmail Babolian
This paper has two purposes. First we present a new definition of the multivariate Padé approximation, a new fast numerical method. Then numerical solution of the one-dimensional (…
A degenerate kernel method for eigenvalue problems of a class of non-compact operators
Hassan Majidian, Esmail Babolian
We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method is used to…