‎in this paper‎, ‎we introduce fractional-order into a model of hiv-1 infection of cd4^+ t--cells‎. ‎we study the effect of ‎the changing the average number of viral particles $n$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎the nonstandard finite difference (nsfd) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order hiv-1‎‎i...

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using ...

A new feedback-based methodology for the implementation of a fractional-order differentiator (FD) is described in this paper. The differentiator can be based on a standard definition of the fractional calculus, such as the Riemann-Liouville or Grunwald-Letnikov definitions. Some methods by which the FD functions can be approximated using a DSP-based implementation (either FIR or IIR) are descri...

Bilgisayar teknolojilerindeki gelişmeler zor ve karmaşık hesaplamalar içeren kesirli matematik alanına olan ilgiyi arttırmıştır. Özellikle, gerçek sistemleri modellemedeki başarısı nedeniyle kontrol alanında çokça yararlanılmaktadır. Pek çok çalışma yapılmasına rağmen matematiği literatürde hala çözümsüz durumlar bulunmaktadır. Kontrol kullanımında karşılaşılan en büyük zorluk analitik çözüm ek...

Abstract This paper presents an unified mathematical and computational framework for mechanics-coupled “anomalous” transport phenomena in porous media. The anomalous diffusion is mainly due to variable fluid flow rates caused by spatially temporally varying permeability. type of behaviour described a fractional pore pressure equation. transient significantly affected the order operators. In sol...

This paper presents a modified numerical scheme for a class of Fractional Optimal Control Problems (FOCPs) formulated in Agrawal (2004) where a Fractional Derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire time domain is divided into several subdomains, and a fractional derivative (FDs) at a time node point is approximated using a modified Grünwald-Letnikov ap...

In this paper, we introduce the nabla fractional derivative and integral on time scales in Riemann-Liouville sense. We also Gr\"unwald-Letnikov Some of basic properties theorems related to calculus are discussed.

The fractional derivative of order α, with 1 < α ≤ 2 appears in several diffusion problems used in physical and engineering applications. Therefore to obtain highly accurate approximations for this derivative is of great importance. Here, we describe and compare different numerical approximations for the fractional derivative of order 1 < α ≤ 2. These approximations arise mainly from the Grünwa...

Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Grünwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotie...

In this paper, a numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is the Grünwald-Letnikov derivative. The detailed error analysis for this algorithm is given, meanwhile, the convergence of the iteration algorithm is proved. Compared with the e...