Mathematical Methods in Engineering

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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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.

• 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
• complexity
• partial differential equations

“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)

• Department of Mathematics, Çankaya University, Ankara, Turkey

  Kenan Taş, Dumitru Baleanu

• Instituto Superior de Engenharia do Porto, Porto, Portugal

  J. A. Tenreiro Machado

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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