Related papers: A Discrete Method to Solve Fractional Optimal Cont…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann-Liouville operators. Using known formulas for computing fractional derivatives of…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
We review recent results obtained to solve fractional order optimal control problems with free terminal time and a dynamic constraint involving integer and fractional order derivatives. Some particular cases are studied in detail. A…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
We provide a fast and simple method to solve fractional variational problems with dependence on Hadamard fractional derivatives. Using a relation between the Hadamard fractional operator and a sum involving integer-order derivatives, we…
This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear…
We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be…
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo…
This article deals with higher order Caputo fractional variational problems with the presence of delay in the state variables and their integer higher order derivatives.
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta…