The book “Fractional calculus: new applications in the understanding of 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 chaotic system of fractional order represented by the Caputo fractional derivative. In Chapter 2, Okundalaye et al. gave a new multistage optimal homotopy asymptotic method for solutions to a pair of fractional optimal control problems. In Chapter 3, Farman et al. studied a complex chaotic financial system of fractional order in price exponent with control and modeling.

The second part of the book, Heat Conduction, consists of two chapters. In Chapter 4, Hristov proposed an attempt to show that Duhamel’s theorem is applicable to 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 variables (superposition version) naturally leads to the 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 in the real line modeled by a derivative of fractional order with a non-singular kernel.

The third section of the book, Computational Methods and Their Illustrative Applications, contains five chapters dealing with 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 behavioral 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 Caputo’s fractional order derivative in the mathematical analysis of a rumor spread model and presented interesting numerical results. In Chapter 9, Veeresha et al. studied a unified approach to the fractional system of equations arising in the biochemical reaction without a singular nucleus. In Chapter 10, Bora et al. investigated the hydromorphodynamic effects induced by an unpowered floating object navigating in an approach channel using the CFD (Computational Fluid Dynamics) process.

Mehmet Yavuz, Ph.D. He is an Associate Professor with Google Scholar h-index: 31 / of 2405 citations and Web of Science h-index: 22 / 1328 citations. He is affiliated with the Faculty of Sciences of Necmettin Erbakan University. He has 58 articles published under his name. 1 international book and contributed to 3 international book chapters. He has been awarded the following awards:

• Award to the scientist with the most publications with international cooperation in 2020, (Necmettin Erbakan University, Turkey)
• The Most Published Scientific Award in the Field of Science/Engineering in 2020 (Necmettin Erbakan University, Turkey)

Keywords:

Fractional calculus, Duhamel’s theorem, Stability analysis, Heat conduction, Chaotic systems, Memory fading, Lyapunov exponents, Adams-Bashforth-Moulton method, Bifurcation maps, Biochemical reaction, Optimal control, Floating object, Analysis of Convergence, Mathematical Modeling, Fractional Finance System, Numerical Simulation, Fixed Point Theorem, Harmonic Source Effect, Dynamic Control, Fractional Hamiltonian Approach.