Fractional-order generalized thermoelastic diffusion theory

doi:10.1007/s10483-017-2230-9

Abstract

Abstract:

The present work aims to establish a fractional-order generalized themoelastic diffusion theory for anisotropic and linearly thermoelastic diffusive media. To numerically handle the multi-physics problems expressed by a sequence of incomplete differential equations, particularly by a fractional equation, a generalized variational principle is obtained for the unified theory using a semi-inverse method. In numerical implementation, the dynamic response of a semi-infinite medium with one end subjected to a thermal shock and a chemical potential shock is investigated using the Laplace transform. Numerical results, i.e., non-dimensional temperature, chemical potential, and displacement, are presented graphically. The influence of the fractional order parameter on them is evaluated and discussed.

Key words: asymptotically regular mappings, p-uniformly convex Banach space, asymptotic center, fixed points, generalized thermoelastic diffusion, Laplace transform, fractional calculus, generalized variational principle

2010 MSC Number:

74F05

Chunbao XIONG, Yanbo NIU. Fractional-order generalized thermoelastic diffusion theory. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1091-1108.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-017-2230-9

https://www.amm.shu.edu.cn/EN/Y2017/V38/I8/1091

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Fractional-order generalized thermoelastic diffusion theory

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