This book collects chapters dealing with some of the theoretical aspects needed to properly discuss the dynamics of complex engineering systems. The book illustrates advanced theoretical development and new techniques designed to better solve problems within the nonlinear dynamical systems. Topics covered in this volume include advances on fixed point results on partial metric spaces, localization of the spectral expansions associated with the partial differential operators, irregularity in graphs and inverse problems, Hyers-Ulam and Hyers-Ulam-Rassias stability for integro-differential equations, fixed point results for mixed multivalued mappings of Feng-Liu type on Mb-metric spaces, and the limit q-Bernstein operators, analytical investigation on the fractional diffusion absorption equation.

• Brings new insights into the field of applied mathematical methods applied in engineering science including nonparametric regression by conic quadratic programming and fractional order filter discretization by particle swarm optimization method
• Demonstrates the existence of a solution for a sum fractional finite difference inclusion;
  
• Presents multiple solutions of second order differential equations.