Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright c ©2005 IFAC

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented an...

Fractional (nonlocal) diffusion equations replace the integer-order derivatives in space and time by fractional-order derivatives. This article considers a nonlocal inverse problem and shows that the exponents of the fractional time and space derivatives are determined uniquely by the data u(t, 0) = g(t), 0 < t < T . The uniqueness result is a theoretical background for determining experimental...

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. Until now, most models have relied on a low-order finite difference method to discretize both the fractional-order space and time derivatives. While the finite difference method is simple and straightforward to solve integer-order differential equ...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...

We propose an anomalous diffusion approach to analyze the electrical impedance response of electrolytic cells using time-fractional derivatives. establish, in general terms, conservation laws connected a modified displacement current entering fractional formulation Poisson–Nernst–Planck (PNP) model. In this new formalism, we obtain analytical expressions for case blocking electrodes and presenc...

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

This paper deals with the method of simulation of fractional order chaotic systems. We present a brief survey of the existing fractional order chaotic systems. These systems are described by three fractional differential equations where order of derivatives is a non-integer, arbitrary order. The total order of chaotic system is less than three. We present an approach where we demonstrate by an ...

A temporal model based on the Biot theory is developed to describe the transient ultrasonic propagation in porous media with elastic structure, in which the viscous exchange between fluid and structure are described by fractional derivatives. The fast and slow waves obey a fractional wave equation in the time domain. The solution of Biot's equations in time depends on the Green functions of eac...