A new class of global fractional-order projective dynamical system with an application

Abstract

In this article, some existence and uniqueness of solutions for a new class of global fractional-order projective dynamical system with delay and perturbation are proved by employing the Krasnoselskii fixed point theorem and the Banach fixed point theorem. Moreover, an approximating algorithm is also provided to find a solution of the global fractional-order projective dynamical system. Finally, an application to the idealized traveler information systems for day-today adjustments processes and a numerical example are given.

Global Mittag-Leffler stability of Fractional-Order Projection Neural Networks with Impulses

“…It is well known that, the projection neural network (dynamical system), captured the desired features of both the variational inequality and the dynamical systems within the same framework, can be used to solve many constrained optimization problems, variational inequality problems, equilibrium point problems, dynamic traffic networks and so on (see, for example, [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and the references therein). Taking into account of the advantages of fractional calculus, Wu and Zou [24], for the first time, proposed a class of fractional order projective dynamical systems.…”

“…On the basic of the linear matrix inequality technique, Li et al [29] obtained some sufficient conditions to ensure the asymptotical stability of the equilibrium point of the addressed projection neural networks. Wu et al [35] investigated a new class of global fractional-order projection dynamical system with delay and obtained existence and uniqueness of solutions for considered dynamical system by using the Krasnoselskii fixed point theorem.…”

Optimality conditions of singular controls for systems with Caputo fractional derivatives

“…It has been shown that models with fractional order derivatives are more adequate than integer order models.The main reason is that fractional derivatives are an excellent tool for describing memory and hereditary properties of various materials and processes. An examples of real systems, we can mention here electrochemical cells, capacitors with irregular (fractal) electrodes, viscoelastic media, disordered semiconductors, plasma and similar media [2,3,5,6,13,16,23,26,28,29,30,31,33,34,35,36,32]. The paper [26] considers the problem of fractional optimal control described by a system of linear differential equations, where its cost function is expressed as the ratio of convex and concave functions.…”

“…Situations with end-time constraints are also considered. In the [32], with the help of the Krasnoselskii and Banach fixed point theorems, existence and uniqueness theorems of solutions were proved for a new class of global projective dynamical systems of fractional order with delay and perturbation. In addition, an approximating algorithm is proposed for finding a solution to a global projective dynamic system of fractional order.…”