Mathematical Methods in Engineering

1. Front Matter

   Pages i-viii

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2. Modelling of the Dynamics of Complex Systems

   1. Front Matter

      Pages 1-1

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   2. New Solutions of the Functional Equations and Their Possible Application in Treatment of Complex Systems

      • R. R. Nigmatullin, B. N. Nougmanov

      Pages 3-24

   3. Empirical Copula in the Detection of Batch Effects

      • Melih Ağraz, Vilda Purutçuoğlu

      Pages 25-39

   4. Finite Element Method for Schnakenberg Model

      • Ozlem Ersoy Hepson, Idris Dag

      Pages 41-51

   5. Fault-Tolerant Control of the (13C) Isotope Separation Cascade

      • Eva-H. Dulf, Cristina-I. Muresan, Clara M. Ionescu

      Pages 53-65

   6. Power Series Transform in Cryptology and ASCII

      • Muharrem Tuncay Gençoğlu, Dumitru Baleanu

      Pages 67-74

   7. The General Form of Maximally Accretive Quasi-differential Operators for First Order

      • Pembe Ipek, Zameddin I. Ismailov

      Pages 75-86

   8. Modeling of Biochemical Networks via Classification and Regression Tree Methods

      • Deniz Seçilmiş, Vilda Purutçuoğlu

      Pages 87-102

   9. Solving the Nonlinear System of Third-Order Boundary Value Problems

      • Ali Akgül, Esra Karatas Akgül, Yasir Khan, Dumitru Baleanu

      Pages 103-119

   10. CG-Lasso Estimator for Multivariate Adaptive Regression Spline

       • Pakize Taylan, Gerhard Wilhelm Weber

       Pages 121-136

3. Fractional Calculus Applications

   1. Front Matter

      Pages 137-137

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   2. Multiscale Characterization and Model for the Dynamic Behavior of Ferroelectric Materials Using Fractional Operators

      • Benjamin Ducharne, Grzegorz Litak, Bin Zhang, Bhaawan Gupta

      Pages 139-152

   3. A Transient Flow of a Non-Newtonian Fluid Modelled by a Mixed Time-Space Derivative: An Improved Integral-Balance Approach

      • Jordan Hristov

      Pages 153-174

   4. Exact Travelling Wave Solutions for Local Fractional Partial Differential Equations in Mathematical Physics

      • Xiao-Jun Yang, Feng Gao, J. A. Tenreiro Machado, Dumitru Baleanu

      Pages 175-191

   5. A New Numerical Approximation of Fractional Differentiation: Upwind Discretization for Riemann-Liouville and Caputo Derivatives

      • Abdon Atangana

      Pages 193-212

   6. Certain Fractional Integrals and Solutions of Fractional Kinetic Equations Involving the Product of S-Function

      • Mehar Chand, Zakia Hammouch, Joshua Kiddy K. Asamoah, Dumitru Baleanu

      Pages 213-244

   7. An Autotuning Method for a Fractional Order PD Controller for Vibration Suppression

      • Cristina I. Muresan, Robin De Keyser, Isabela R. Birs, Silviu Folea, Ovidiu Prodan

      Pages 245-256

4. Back Matter

   Pages 257-264

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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.

• complex systems
• Ant Colony Optimization Algorithm
• salesman problem
• Fractal Time Motion
• Finite Element Method
• Schnackenberg Model
• Empirical Copula
• Riemann-Liouville and Caputo derivatives
• Fractional Kinetic Equations
• Conformable Adomian Decomposition Method
• Conformable Differential Transform Method
• Systems of Differential Equations
• complexity

• Department of Mathematics, Cankaya University, Ankara, Turkey

  Kenan Taş

• Department of Mathematics, Çankaya University, Ankara, Turkey

  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 within the Department of Electrical Engineering, Isep-Institute of Engineering, Polytechnic of Porto, Portugal.

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