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Mathematical Methods in Engineering

Theoretical Aspects

  • Book
  • © 2019

Overview

Editors:
  1. Kenan Taş

    1. Department of Mathematics, Çankaya University, Ankara, Turkey

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  2. Dumitru Baleanu

    1. Department of Mathematics, Çankaya University, Ankara, Turkey

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  3. J. A. Tenreiro Machado

    1. Instituto Superior de Engenharia do Porto, Porto, Portugal

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  • 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

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-viii
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  2. Fixed Point Theory and Applications

    1. Front Matter

      Pages 1-1
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    2. Advances on Fixed Point Results on Partial Metric Spaces

      • Erdal Karapınar, Kenan Taş, Vladimir Rakočević
      Pages 3-66

    3. Fixed Point Results for Mixed Multivalued Mappings of Feng-Liu Type on M b -Metric Spaces

      • Hakan Şahin, Ishak Altun, Duran Türkoğlu
      Pages 67-80

    4. Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations

      • L. P. Castro, A. M. Simões
      Pages 81-94

  3. New Mathematical Ideas

    1. Front Matter

      Pages 95-95
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    2. Exact Solutions, Lie Symmetry Analysis and Conservation Laws of the Time Fractional Diffusion-Absorption Equation

      • Mir Sajjad Hashemi, Zahra Balmeh, Dumitru Baleanu
      Pages 97-109

    3. Integral Balance Approach to 1-D Space-Fractional Diffusion Models

      • Jordan Hristov
      Pages 111-131

    4. Fractional Order Filter Discretization by Particle Swarm Optimization Method

      • Ozlem Imik, Baris Baykant Alagoz, Abdullah Ates, Celaleddin Yeroglu
      Pages 133-144

    5. On the Existence of Solution for a Sum Fractional Finite Difference Inclusion

      • Vahid Ghorbanian, Shahram Rezapour, Saeid Salehi
      Pages 145-160

    6. Comparison on Solving a Class of Nonlinear Systems of Partial Differential Equations and Multiple Solutions of Second Order Differential Equations

      • Ali Akgül, Esra Karatas Akgül, Yasir Khan, Dumitru Baleanu
      Pages 161-190

    7. Effect of Edge Deletion and Addition on Zagreb Indices of Graphs

      • Muge Togan, Aysun Yurttas, Ahmet Sinan Cevik, Ismail Naci Cangul
      Pages 191-201

    8. The Limit q-Bernstein Operators with Varying q

      • Manal Mastafa Almesbahi, Sofiya Ostrovska, Mehmet Turan
      Pages 203-215

    9. Localization of the Spectral Expansions Associated with the Partial Differential Operators

      • Abdumalik Rakhimov
      Pages 217-233

    10. Energy Decay in a Quasilinear System with Finite and Infinite Memories

      • Muhammad I. Mustafa
      Pages 235-256

    11. A Modified and Enhanced Ant Colony Optimization Algorithm for Traveling Salesman Problem

      • Leila Eskandari, Ahmad Jafarian, Parastoo Rahimloo, Dumitru Baleanu
      Pages 257-265

    12. A Note on the Upper Bound of Average Distance via Irregularity Index

      • Nihat Akgunes, Ismail Naci Cangul, Ahmet Sinan Cevik
      Pages 267-271

  4. Back Matter

    Pages 273-278
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Keywords

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.

Reviews

“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)

Editors and Affiliations

  • Department of Mathematics, Çankaya University, Ankara, Turkey

    Kenan Taş, Dumitru Baleanu

  • Instituto Superior de Engenharia do Porto, Porto, Portugal

    J. A. Tenreiro Machado

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.

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