Fractional control of heat diffusion systems

Abstract

The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

Synchronization of dynamical systems of different orders and different dimensions

“…Several other significant analysis have also been done on fractional differential equations [9]- [11]. In several different fields applications of fractional calculus can be easily seen like biology, chemistry and bioengineering etc [12]- [14]. Three decades ago when Pecora and Carroll [15] presented a new finding in the field of chaos which is known as synchronization, inclination of researchers towards this branch has always been immense.…”

Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients

“…Some applications can be found in image proRishi Kumar Pandey: Jaypee University of Engineering & technology Guna, M.P., India, E-mail: rishipandey.9@rediffmail.com *Corresponding Author: Hradyesh Kumar Mishra: Jaypee University of Engineering & technology Guna, M.P., India, E-mail: hk.mishra@juet.ac.in cessing, plasma physics, nonlinear control theory, biological modelling, and astrophysics etc. [8][9][10][11][12][13][14][15][16]. Hu et al [17] provide the fractal space-time scales observation based on a smaller threshold model in micro and nano scale with smoothness.…”

Legendre multiwavelet collocation method for solving the linear fractional time delay systems

“…It has also been shown that materials with memory and hereditary effects and dynamical processes including gas diffusion and heat conduction in fractal porous media can be modeled by fractional order models better than integer models [5]. Fractional control problems have also been under development in the recent years and there exist several publications in this field such as [6][7][8]. Fractional time delay systems have also been in center of attention of some authors.…”