Related papers: Approximate Solution to the Fractional Second Type…
Lane-Emden equation could be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic index and . In the present paper, a series solution for…
In this paper, approximate solutions for a class of fractional Lane - Emden type equations based on the series expansion method are presented. Various examples are introduced and discussed. The recurrence relation for the components of the…
Lane Emden differential equation of the polytropic gas sphere could be used to construct simple models of stellar structures, star clusters and many configurations in astrophysics. This differential equation suffers from the singularity at…
We establish a Liouville type theorem for the fractional Lane-Emden system: \begin{eqnarray*} \left\{\begin{array}{l@{\quad }l} (-\Delta)^\alpha u=v^q&{\rm in}\,\,\R^N,\\ (-\Delta)^\alpha v=u^p&{\rm in}\,\,\R^N, \end{array} \right.…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional…
In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian…
Our purpose of this paper is to study the nonexistence of nonnegative very weak solutions of \begin{equation}\label{eq 0.1} \displaystyle (-\Delta)^\alpha u = u^p+\nu\quad {\rm in}\quad \Omega,\qquad\ u=g\quad {\rm in}\quad \mathbb{…
In this paper, we establish Liouville type theorems for stable solutions on the whole space $\mathbb R^N$ to the fractional elliptic equation $$(-\Delta)^su=f(u)$$ where the nonlinearity is nondecreasing and convex. We also obtain a…
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. It is based on…
Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a…
In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
The Lane-Emden type equations are employed in the modelling of several phenomena in the areas of mathematical physics and astrophysics . In this paper a new numerical method is applied to investigate some well-known classes of Lane-Emden…
In this paper a fractional differential equation of the Euler-Lagrange / Sturm-Liouville type is considered. The fractional equation with derivatives of order $\alpha \in \left( 0,1 \right]$ in the finite time interval is transformed to the…
The isothermal gas sphere is well known as a powerful tool to model many problems in astrophysics, physics, chemistry, and engineering. This singular differential equation has not an exact solution and solved only by numerical and…
The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the…
In this paper, the Lie symmetry analysis is proposed for a space-time convection-diffusion fractional differential equations with the Riemann-Liouville derivative by (2+1) independent variables and one dependent variable. We find a…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…