Abstract
In this article, the multistage homotopy perturbation method (MHPM) is applied for solving differential systems with fractional order derivatives in the Caputo sense. This method is a modification of the standard homotopy perturbation method (HPM). A fractional Lorenz system as an application is presented for which some numerical comparisons between the (MHPM) and (HPM) with the 4th order Runge-Kutta method (RK4). The results reveal that the used pre-mentioned procedure (MHPM) is a reliable and an effective tool for constructing an accurate approximate solution for the fractional Lorenz system.
Highlights
We extend the application of (HPM) to solve a system of fractional order differential equations of the form: Dαiyi = fi(t,y1,y2,···,yn) with the initial condition: where L is a linear operator, while N is a nonlinear operator, B is a boundary operator, Γ is the boundary of the domain Ω and f(r) is a known analytic function
In table (1), we present the absolute errors between the 10-term (MHPM) solutions and the 10-term homotopy perturbation method (HPM) solutions and the (RK4) solutions on time step h = 0.01 and α = 1 for r = 28
The main aim of this work is to use the multistage homotopy perturbation method (MHPM) which is a modification to the standard (HPM) to solve the fractional Lorenz system
Summary
Introduction It is well-known that the Lorenz system [1] which is an idealized model describing turbulent flow in the atmosphere. The atmosphere is just one of many hydrodynamical systems which exhibit a variety of solution behavior: some flows are steady, others oscillate between two or more states and still others vary in an irregular manner. This last class of behavior in a fluid is known as turbulence or in more general systems as chaos.
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