© 2019

Mathematical Methods in Engineering

Theoretical Aspects

  • Kenan Taş
  • Dumitru Baleanu
  • J. A. Tenreiro Machado

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 23)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Fixed Point Theory and Applications

    1. Front Matter
      Pages 1-1
    2. Erdal Karapınar, Kenan Taş, Vladimir Rakočević
      Pages 3-66
    3. Hakan Şahin, Ishak Altun, Duran Türkoğlu
      Pages 67-80
  3. New Mathematical Ideas

    1. Front Matter
      Pages 95-95
    2. Ozlem Imik, Baris Baykant Alagoz, Abdullah Ates, Celaleddin Yeroglu
      Pages 133-144
    3. Vahid Ghorbanian, Shahram Rezapour, Saeid Salehi
      Pages 145-160
    4. Muge Togan, Aysun Yurttas, Ahmet Sinan Cevik, Ismail Naci Cangul
      Pages 191-201
    5. Manal Mastafa Almesbahi, Sofiya Ostrovska, Mehmet Turan
      Pages 203-215
    6. Leila Eskandari, Ahmad Jafarian, Parastoo Rahimloo, Dumitru Baleanu
      Pages 257-265
    7. Nihat Akgunes, Ismail Naci Cangul, Ahmet Sinan Cevik
      Pages 267-271
  4. Back Matter
    Pages 273-278

About this book


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.


Engineering Mathematics partial metric spaces spectral expansions Irregularity in Graphs and Inverse Problems Hyers-Ulam Stability Hyers-Ulam-Rassias Stability Integro-Differential Equations Mb-metric spaces q-Bernstein operators fractional diffusion-absorption equation Nonparametric Regression by Conic Quadratic Programming Particle Swarm Optimization Method

Editors and affiliations

  • Kenan Taş
    • 1
  • Dumitru Baleanu
    • 2
  • J. A. Tenreiro Machado
    • 3
  1. 1.Department of MathematicsÇankaya UniversityAnkaraTurkey
  2. 2.Department of MathematicsÇankaya UniversityAnkaraTurkey
  3. 3.Instituto Superior de Engenharia do PortoPortoPortugal

About the editors

Dr. Kenan Tas is a Professor and Provost Of The Çankaya University, Ankara, Turkey. Dr. Dumitru Baleanu is a Professor with Institute of Space Sciences, Magurele-Bucharest, Romania and Visiting Staff Member At Cankaya University, Ankara, Turkey.  Dr. J. A. Tenreiro Machado is Principal Coordinator Professor Institute of Engineering, Polytechnic of Porto, Portugal.

Bibliographic information

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“All the papers are presented as theorems, and there are no problems to show readers their application. Each chapter has extensive citations. Some of the theorems have derivations that are illustrated by graphs. … Summing Up: Recommended. Researchers, faculty, and professionals.” (N. Sadanand, Choice, Vol. 56 (11), July, 2019)