@article{Nuruddeen2023, 
author = {Rahmatullah Ibrahim Nuruddeen and J. F. Gómez-Aguilar and José R. Razo-Hernández},
title = {Fractionalizing, coupling and methods for the coupled system of two-dimensional heat diffusion models},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {11180-11201},
keywords = {fractionalization, couplings, integral transforms, Laplace decomposition method, heat diffusion models},
url = {https://www.sciopen.com/article/10.3934/math.2023566},
doi = {10.3934/math.2023566},
abstract = {The present manuscript gives an overview of how two-dimensional heat diffusion models underwent a fractional transformation, system coupling as well as solution treatment. The governing diffusion models, which are endowed with Caputo's fractional-order derivatives in time    t, are suitably coupled using the (1) convection phenomenon, (2) interfacial coupling by considering the mechanism of a double-layered bar, and the (3) nonlinear coupling due to temperature-dependent thermal diffusivities. Semi-analytical and analytical methods are considered for the solution treatment. Moreover, we seek a computational environment to graphically illustrate the systems' response to different fractional orders in each case through the determined diffusional fields. Besides, we supply certain concluding notes at the end.}
}