As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the description and analysis of real dynamical systems than integer-order models, because their total entropy is greater than in integer-order models wi...

Based on the fractional order of nonlinear system for love model with a periodic function 10 as an external force, analyzed the characteristics of the chaotic dynamic in this study. The 11 relationship between the chaotic dynamic of the fractional-love model with the external force and 12 the fractional-order system was analyzed when the parameters are fixed. Further, we also studied 13 the rel...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

Grey system is a theory which specially studies poor information, and it possesses wide suitability. The parameters of multivariable grey FMGM(1,n) model with the fractional order accumulation can reflect the restricted and affected multi-variables relation with one another. We start by constructing background values based on vector continued fractions theory by using rational interpolation wit...

This paper presents the application of a direct Fractional Order Model Reference Adaptive Controller (FOMRAC) to an Automatic Voltage Regulator (AVR). A direct FOMRAC is a direct Model Reference Adaptive Control (MRAC), whose controller parameters are adjusted using fractional order differential equations. Four realizations of the FOMRAC were designed in this work, each one considering differen...

In this paper, we study measurement of sensitivity for changes of violations in the aspiration level for the fuzzy multiobjective linear fractional programming problem. c © 2001 Elsevier Science B.V. All rights reserved.

This paper describes our experimental testing of linear viscoelastic creep behaviours in HamiMelon. Experimental data shows that HamiMelon has complex viscoelastic property which cannot be well described by the standard model. Consequently, this study develops a fractional derivative model to describe such complex viscoelastic creep behaviours of Hami Melon. The analytical creep function of the...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...