The book “Fractional Calculus: New Applications in Understanding Nonlinear Phenomena” contains ten chapters in three sections. The first section, Chaotic Systems and Control, contains three chapters. In Chapter 1, Sene proposed a numerical procedure and its applications to a fractional-order chaotic system represented with the Caputo fractional derivative. In Chapter 2, Okundalaye et al. gave a new multistage optimal homotopy asymptotic method for solutions to a couple of fractional optimal control problems. In Chapter 3, Farman et al. studied a complex chaotic fractional-order financial system in price exponent with control and modelling.
The second part of the book, Heat Conduction, contains two chapters. In Chapter 4, Hristov proposed an attempt to demonstrate that the Duhamel theorem applicable for time-dependent boundary conditions (or time-dependent source terms) of heat conduction in a finite domain and the use of the Fourier method of separation of variable (superposition version) naturally leads to appearance of the Caputo–Fabrizio operators in the solution. In Chapter 5, Avcı and İskender Eroğlu considered the oscillatory heat transfer due to the Cattaneo–Hristov model on the real line modelled by a fractional-order derivative with a non-singular kernel.
The third section of the book, Computational Methods and Their Illustrative Applications, contains five chapters related to different types of real-life problems. In Chapter 6, Ghoreishi et al. applied the optimal homotopy analysis method for a nonlinear fractional-order model to HTLV-1 infection of CD4+ T-cells. In Chapter 7, Durur et al. investigated the behavior analysis and asymptotic stability of the traveling wave solution of the Kaup-Kupershmidt equation with the conformable operator. In Chapter 8, Baishya et al. took into account the Caputo fractional order derivative in the mathematical analysis of a rumor-spreading model and presented interesting numerical results. In Chapter 9, Veeresha et al. studied a unified approach for the fractional system of equations arising in the biochemical reaction without a singular kernel. In Chapter 10, Bora et al. investigated the hydro-morphodynamic effects induced by a non-powered floating object navigating in an approach channel using the CFD (Computational Fluid Dynamics) process.
About the editor:
Mehmet Yavuz, Ph.D. is an Associate Professor having h-Index from Google Scholar: 31 / from 2405 citations and h-Index from Web of Science: 22 / 1328 citations. He is affiliated with Necmettin Erbakan University, Faculty of Science. He has 58 articles published under his name. 1 international book and contributed in 3 international book chapters. He had been awared the following awards:
- Award for the most publishing scientist with international cooperation in 2020, (Necmettin Erbakan University, Turkey)
- The most published scientist award in the field of science / engineering in 2020, (Necmettin Erbakan University, Turkey)
Keywords:
Fractional Calculus, Duhamel Theorem, Stability Analysis, Heat Conduction, Chaotic Systems, Fading Memory, Lyapunov Exponents, Adams-Bashforth-Moulton method, Bifurcation Maps, Biochemical Reaction, Optimal Control, Floating Object, Convergence Analysis, Mathematical Modelling, Fractional-order Financial System, Numerical Simulation, Fixed Point Theorem, Harmonic Source Effect, Dynamical Control, Fractional Hamiltonian Approach.
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