Fractionalizing, coupling and methods for the coupled system of two-dimensional heat diffusion models

Rahmatullah Ibrahim Nuruddeen; J. F. Gómez-Aguilar; José R. Razo-Hernández; Rahmatullah Ibrahim Nuruddeen; J. F. Gómez-Aguilar; José R. Razo-Hernández

doi:10.3934/math.2023566

AIMS Mathematics

2023, Volume 8, Issue 5: 11180-11201. doi: 10.3934/math.2023566

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Research article Special Issues

Fractionalizing, coupling and methods for the coupled system of two-dimensional heat diffusion models

1.
Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria
2.
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos, México
3.
Departamento de Ingeniería Electromecánica, Tecnológico Nacional de México, Instituto Tecnológico Superior de Irapuato (ITESI), Carr. Irapuato-Silao km 12.5, Colonia El Copal, C.P. 36821, Irapuato, Guanajuato, México

Received: 24 December 2022 Revised: 16 February 2023 Accepted: 22 February 2023 Published: 09 March 2023
MSC : 26A33, 34A08, 34K37, 35R11

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.
- fractionalization,
- couplings,
- integral transforms,
- Laplace decomposition method,
- heat diffusion models
Citation: Rahmatullah Ibrahim Nuruddeen, J. F. Gómez-Aguilar, José R. Razo-Hernández. Fractionalizing, coupling and methods for the coupled system of two-dimensional heat diffusion models[J]. AIMS Mathematics, 2023, 8(5): 11180-11201. doi: 10.3934/math.2023566

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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.

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