Mathematical Methods in Engineering Applications in Dynamics of Complex Systems

This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations.

New solutions of the functional equations and their possible application in treatment of complex systems.- A modified and enhanced Ant Colony Optimization Algorithm for traveling salesman problem.- Fractal Time Motion on Particle Diffusion.- An Autotuning Method for a Fractional Order PD Controller for Vibration Suppression.- Advanced control strategies of the 13C isotope separation columns cascade.- Multiscale characterization and model for the dynamic behavior of ferroelectric materials using fractional operators.- Energy decay in a quasilinear system with finite and infinite memories.- Finite Element Method for Schnackenberg Model.- Empirical Copula in the Detection of Batch Effects.- Exact traveling wave solutions for local fractional partial differential equations in mathematical physics.- A new numerical approximation of fractional discretization: Upwind discretization for Riemann-Liouville and Caputo derivatives.- Certain Fractional Integrals and Solutions of Fractional Kinetic Equations involving the product of S-function.- Application of Conformable Adomian Decomposition Method and Conformable Differential Transform Method to Systems of Differential Equations