We prove a Noether’s theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.

This opening lecture is intended to serve as a propaedeutic for the papers to be presented at this conference whose nonhomogeneous audience includes scientists, mathematicians, engineers and educators. This expository and developmental lecture, a case study of mathematical growth, surveys the origin and development of a mathematical idea from its birth in intellectual curiosity to applications....

This book investigates the fractional calculus-based approaches and their benefits to adopting in complex real-time areas

The prime aim of the present paper is to continue developing theory tempered fractional integrals and derivatives a function with respect another function. This combines calculus $\Psi$-fractional calculus, both which have found applications in topics including continuous time random walks. After studying basic $\Psi$-tempered operators, we prove mean value theorems Taylor's for Riemann--Liouvi...

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether’s theorem to fractional optima...

Abstract Fractional calculus is a branch of classical mathematics, which deals with the generalization of operations of differentiation and integration to fractional order. Such a generalization is not merely a mathematical curiosity but has found applications in various fields of physical sciences. In this paper, we review the definitions and properties of fractional derivatives and integrals,...

In this paper we introduce the different types of the Fractional Order PID controllers and presented some of its application to Industry and robotics Key-Words: Fractional Order Calculus, Differintegration, Fractional Order Controllers, Control Theory, Control Systems, PID controller, tuning, auto-tuning.

Fractional calculus has played an important role in the fields of mathematics, physics, electronics, mechanics, and engineering recent years [...]

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.

Fractional differential equations started to have important applications in various fields of science and engineering involving dynamics of complex phenomena. Finding new methods to solve the fractional differential equations is an open issue in the area of fractional calculus. In this paper the homotopy perturbation method is used to find an analytic approximate solution for the coupled Lotka-...