<p style='text-indent:20px;'>Ordinary differential equations are converted into a constrained optimization problems to find their approximate solutions. In this work, an algorithm is proposed by applying particle swarm (PSO) solution of ODEs based on expansion approximation. Since many cases linear and nonlinear have singularity point, Padé approximant which fractional employed for more a...

In this work, we investigate astrophysical systems in a Newtonian regime using anisotropic matter. For purpose, considered that both radial and tangential pressures satisfy generalized Chaplygin-type equation of state. Using model, found the Lane–Emden for system solved it numerically several sets parameters. Finally, explored mass supported by physical compared with Chandrasekhar mass.

Abstract This paper examines the general formalism and applications of isotropic as well anisotropic polytropic stars in curvature-matter coupled gravity. For this purpose, we consider static spherical Schwarzschild spacetimes interior exterior regions, respectively. We use two equations state to obtain physically viable solutions field equations. The hydrostatic equilibrium Lane-Emden are deve...

Singular initial value problems are investigated. We extend a decomposition method for di¤erent type Emden-Fowler-like equations. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method. The solutions are constructed in the form of a convergent series.

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method could be proved are formulated and elaborated. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the li...

In this paper, we first establish decay estimates for the fractional and higher-order H\'enon-Lane-Emden systems by using a nonlocal average integral estimates, which deduce result of non-existence. Next, apply method scaling spheres introduced in \cite{DQ2} to derive Liouville type theorem. We also construct an interesting example on super $\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).