A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...

The present work demonstrates the connections between Burgers, diffusion, and Schroedinger's equations. starting point is a formulation of stochastic mechanics, which modeled along lines scale relativity theory. resulting statistical description obeys Fokker-Planck equation. This paper further connection two approaches, embodied by study Burgers equation, from this perspective appears as geodes...

This survey is an introduction to well-posed linear time-invartiant (LTI) systems for non-specialists. We recall the more general concept of a system node, classical and generalized solutions of system equations, criteria for well-posedness, the subclass of regular linear systems, some of the available linear feedback theory. Motivated by physical examples, we recall the concepts of impedance p...

Optimal control problems (OCP) for Burgers equation are important for the development of numerical methods for optimal control of more complicated models in fluid dynamics such as Navier-Stokes equations. In this work, we analyze variant preconditioners for the saddle point problem arising from boundary control of unsteady Burgers equation. As for a solution approach for the discretization of t...

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we develope...