In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

Keywords: fractal geometry, fractional derivative, fractional Fourier transform, fractional power of a matrix, self similarity, complex partial differential equation, broadband ultrasound, frequency-dependent attenuation, time domain. 1. Backgrounds The rational behind this model is schematically illustrated below: Fractal geometry (irregular soft tissues) → Fractional Fourier transform (freque...

The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependence, considered as an intermediate step between the standard (Bm) fractional (fBm). mixed linear combination Bm independent sfBm, called (msfBm), keeps features of sfBm adding semi-martingale property for H>3∕4, suitable candidate to use price fluctuatio...

A fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model. Also different from other models, a model with the order 2 α is discussed. We are expecting an acceleration in feelings; that is why we increase the order of the derivative between 1 < 2α ≤ 2. Stability analysis of the fractional-order nonlinear...

The introduction of fractional-order derivatives to epidemiological compartment models, such as SIR models, has attracted much attention. When this introduction is done in an ad hoc manner, it is difficult to reconcile parameters in the resulting fractional-order equations with the dynamics of individuals. This issue is circumvented by deriving fractional-order models from an underlying stochas...

A model of fractional-order of thermoelasticity is applied to study a 2D problem of mode-I crack in a fibre-reinforced thermal environment. The crack is under prescribed distributions of heat and pressure. The normal mode analysis is applied to deduce exact formulae for displacements, stresses, and temperature. Variations of field quantities with the axial direction are illustrated graphically....

Fractional order dynamic model could model various real materials more adequately than integer order ones and provide a more adequate description of many actual dynamical processes. Fractional order controller is naturally suitable for these fractional order models. In this paper, a fractional order PID controller design method is proposed for a class of fractional order system models. Better p...

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. W...