30 citations · 31 across the 2 of their papers we have counts for
5 papers
Discontinuous Galerkin methods for fractional elliptic problems
Tarek Aboelenen
We provide a mathematical framework for studying different versions of discontinuous Galerkin (DG) approaches for solving 2D Riemann-Liouville fractional elliptic problems on a fin…
A direct discontinuous Galerkin method for fractional convection-diffusion and Schrödinger type equations
Tarek Aboelenen
A direct discontinuous Galerkin (DDG) finite element method is developed for solving fractional convection-diffusion and Schrödinger type equations with a fractional Laplacian oper…
Local discontinuous Galerkin method for distributed-order time and space-fractional convection-diffusion and Schrödinger type equations
Tarek Aboelenen
Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous…
A high-order nodal discontinuous Galerkin method for nonlinear fractional Schrödinger type equations
Tarek Aboelenen
We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schrödinger equation and the strongly coupled nonlinear Riesz space fractional Sch…
Spectral Theory and Numerical Approximation for Singular Fractional Sturm-Liouville eigen-Problems on Unbounded Domain
T. Aboelenen, H. M. El-Hawary
In this article, we first introduce a singular fractional Sturm-Liouville eigen-problems (SFSLP) on unbounded domain. The associated fractional differential operators in these prob…