Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative

By Jordan Hristov. 2016

258 citations recorded by the source corpus.

Starting from the Cattaneo constitutive relation with a Jeffrey’s kernel the derivation of a transient heat diffusion equation with relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been developed. This approach allows seeing the physical background of the newly defined Caputo-Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/98f40b78ea2c44ba3d29face4b9a1fb3c290ec5a

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel (2020, background): “Some interesting studies such as [17, 10, 2, 3, 18, 25, 24, 8] have been resulted in the sense of the CFO.”
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “For example, FD with respect to the kernel of the exponential function in the sense of the Caputo type was firstly reported in [17-24] and FD with the aid of the kernel of the exponential function in the sense of the Riemann-Liouville type was proposed in [25] and developed in [26].”
The Role of Fractional Time-Derivative Operators on Anomalous Diffusion (2017, methodology): “[49] J. Hristov, Therm.”