in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

Two classes of partially known systems are considered in this note; both of them have a fractional parameterization of the unknowns. The first class consists of nonlinear systems whose uncertainties are bounded by a function of fractional parameterization, and the second class compromises those systems whose unknown dynamics can directly, but nonlinearly, be parameterized. It is shown that adap...

The aim of this study is to investigate multi-dimensional vector variational problems considering data uncertainty in each the objective functional and constraints. We establish robust necessary sufficient efficiency conditions such that any feasible solution could be weakly efficient for under consideration. Emphatically, we present scalar, vector, fractional by using notion a convex functional.

This paper presents a toolbox developed in Matlab for analysis and design of fractional order control systems that can be used in advanced control courses within the context of master and doctorate education. The toolbox includes a user friendly interface for every function. One can obtain time and frequency analysis tools both for the fractional order control systems and fractional order contr...

This paper applies fractional order PID controller to torsional system’s backlash vibration suppression control, in which the order k of D controller can not only be integer but also be any real number. In order to improve control system’s robustness against backlash non-linearity, several methods have been proposed. However their design processes are very complicated. In this paper, a clear an...

this paper addresses synchronizing two coupled chaotic fitzhugh–nagumo (fhn) neurons with weakly gap junction under external electrical stimulation (ees). to transmit information among coupled neurons, by generalization of the integer-order fhn equations of the coupled system into the fractional-order in frequency domain using crone approach, the behavior of each coupled neuron relies on its pa...

This paper addresses synchronizing two coupled chaotic FitzHugh–Nagumo (FHN) neurons with weakly gap junction under external electrical stimulation (EES). To transmit information among coupled neurons, by generalization of the integer-order FHN equations of the coupled system into the fractional-order in frequency domain using Crone approach, the behavior of each coupled neuron relies on its pa...