The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

The paper is dedicated to analytical and algebraic approaches to the problem of the integration of ordinary differential equations. The first part is devoted to linear ordinary differential equations of the second and nth orders, while the second deals with nonlinear ordinary differential equations. Factorization of nonlinear equations of the second and the third orders both through commutative...

The linearization of complex ordinary differential equations is studied by extending Lie’s criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations implies the linearizability of systems of partial differential equations corresponding to those complex ordinary differential equations. The invertible comp...

In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...

in this paper we propose a method for solving some well-known classes of lane-emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. the proposed approach is based on an unsupervised combined articial neural networks (ucann) method. firstly, the trial solutions of the differential equations are written in the form of feed-forward neural networks co...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...

the paper presents the semi-numerical solution for the magnetohydrodynamic (mhd) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. the governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (node) by using a classical similarity transformation along with appropriate boundary cond...

In this study,differential transform method (DTM) is applied to linear and nonlinear system of ordinary differential equations. If the system considered has a solution in terms of the series expansion of known functions,this powerful method catches the exact solution.So as to show this capability and robustness, some systems of ordinary differential equations are solved as numerical examples.