Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional systems. Due to the extra free parameter order α, fractional-order based methods provide additional degree of freedom in optimization performance. Not surpr...

Landscape metrics rely on classifications of remote sensing data, and errors inherent to the classification scheme will be propagated into any spatial pattern results. This issue is compounded for metrics derived from sub-pixel unmixing techniques, since a universal method for assessing the certainty of these soft classifications has not yet been accepted. This study investigates the role of su...

This study presents the Homotopy Perturbation Method (HPM) for nonlinear fractional reaction diffusion systems, derivatives are described in caputo's' operator. The focus on three systems of equations one, two and dimensions, this method, solution considered as sum an infinite series. Which converges rapidly to exact solution. is no need use Adomian's polynomials calculate terms; we test propos...

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in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

It is well known that fractional differential equations appeared more and more frequently in different research areas, such as fluid mechanics, viscoelasticity, biology, physics, engineering and other areas of science [1-30]. Considerable attention have been spent in recent years to develop techniques to look for solutions of nonlinear fractional partial differential equations (NFPDEs). Consequ...

In this paper, we propose a procedure to achieve rational approximation to arbitrary fractional order linear time invariant (FO-LTI) systems with sub-optimum H2-norm. Through illustrations, we show that the rational approximation is simple and effective. It is also demonstrated that this sub-optimum approximation method is effective in designing integer order controllers for FO-LTI systems in g...

In this article, we introduce the concept of fractional wavelet transform. Using a two-channel unbalanced lifting structure it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT , respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+ 1/q = 1. The low-band...