Abstract
We study the heat conduction with a general form of a constitutive equation containing fractional derivatives of real and complex order. Using the entropy inequality in a weak form, we derive sufficient conditions on the coefficients of a constitutive equation that guarantee that the second law of thermodynamics is satisfied. This equation, in special cases, reduces to known ones. Moreover, we present a solution of a temperature distribution problem in a semi-infinite rod with the proposed constitutive equation.
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Atanackovic, T.M., Pilipovic, S. On a constitutive equation of heat conduction with fractional derivatives of complex order. Acta Mech 229, 1111–1121 (2018). https://doi.org/10.1007/s00707-017-1959-4
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DOI: https://doi.org/10.1007/s00707-017-1959-4