Abstract
In this paper, we make use of the relatively new analytical technique, the homotopy decomposition method (HDM), to solve a system of fractional nonlinear differential equations that arise in the model for HIV infection of CD4+ T cells and attractor one-dimensional Keller-Segel equations. The technique is described and illustrated with a numerical example. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward.
Highlights
Fractional calculus has been used to model physical and engineering processes, which are found to be best described by fractional differential equations [ ]
Major topics include anomalous diffusion, vibration and control, continuous time random walk, Levy statistics, fractional Brownian motion, fractional neutron point kinetic model, power law, Riesz potential, fractional derivative and fractals, computational fractional derivative equations, nonlocal phenomena, history-dependent process, porous media, fractional filters, biomedical engineering, fractional phase-locked loops, fractional variational principles, fractional transforms, fractional wavelet, fractional predator-prey system, soft matter mechanics, fractional signal and image processing, singularities analysis and integral representations for fractional differential systems, special functions related to fractional calculus, non-Fourier heat conduction, acoustic dissipation, geophysics, relaxation, creep, viscoelasticity, rheology, fluid dynamics, and chaos
The purpose of this paper is to make use of the homotopy decomposition method (HDM) [, ], a relatively new analytical technique, to solve a system of fractional partial differential equations that arise in the model for HIV infection of CD + T cells and attractor one-dimensional Keller-Segel equations
Summary
Fractional calculus has been used to model physical and engineering processes, which are found to be best described by fractional differential equations [ ]. We consider a fractional case of the HIV infection model of CD + T cells examined in [ ]. Guy Jumarie (see [ , ]) proposed a simple alternative definition to the Riemann-Liouville derivative (x – t)n–α– f (t) – f ( ) dt. His modified Riemann-Liouville derivative seems to have advantages over both the standard Riemann-Liouville and the Caputo fractional derivatives: it is defined for arbitrary continuous (non-differentiable) functions, and the fractional derivative of a constant is equal to zero. Definition The Riemann-Liouville fractional integral operator of order α ≥ , of a function f ∈ Cμ, μ ≥ – , is defined as.
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