Abstract
This special collection is based on interdisciplinary theoretical studies, computational algorithm development, and applications of thermal systems. Related areas such as nonlinear modeling, simulation, identification, and control are also included. Moreover, this special collection aims to provide a discussion on diverse branches of mathematics, especially in fractional calculus operator and its applications in mechanical engineering, science, and statistics.
The paper of Baleanu et al. is devoted to the application of the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo–Fabrizio derivative. A detailed comparison of the obtained results was reported. All computations were done using Mathematica. The paper by Bie et al. contains an interesting application of modeling and controlling self-reconfiguration of modular robots. They extend L-systems to the self-reconfiguration process of modules robots.
On the other hand, Kilicman and Ahmood study the matrix fractional differential equations and the exact solution for the system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices in their paper.
The paper by Pourbashash et al. is based on a numerical efficient method for fractional mobile/immobile equation. At the same time, Su et al.’s study is based on the fractal derivative, and a robust viscoelastic element—fractal dashpot—is proposed to characterize the rheological behaviors of non-Newtonian fluid.
In the paper by Ye et al., based on the thermo-mechanical coupling effect that commonly exists in the loading zone of angular-contact ball bearings while the bearings are operated, several process parameters are analyzed, including coordination condition of thermal expansion–deformation load, interaction relationship of contact stress, friction heat, and temperature raised in the loading zone of bearings.
All the published papers are high in quality, contain original research results, and contribute to the theory of fractional calculus and thermal systems.