Analysis of Heat Conduction and Anomalous Diffusion in Fractional Calculus

Dear Colleagues,

Fractional calculus is a powerful tool for modeling physical phenomena in which classical integer-order calculus cannot capture the system's complexity. One such area where fractional calculus has been found to be particularly useful is the study of heat conduction and anomalous thermal diffusion. The classical Fourier law of heat conduction assumes that the heat flux is proportional to the temperature gradient, which leads to a linear heat conduction equation. However, this law can only sometimes accurately describe heat conduction in complex materials. The use of fractional differential operators in the heat conduction equation has been shown to be effective in modeling non-local and memory effects in heat conduction. This behavior has been observed in many physical systems, including biological systems and porous media. Thus, fractional calculus in thermal conduction and diffusion is an interesting research area that provides useful tools to investigate the anomalous thermodynamic process in several fields, such as physics, fluid dynamics, chemistry, and biology, among others. Its relevance lies in its ability to capture the complexity of these systems and provide a more accurate description of their behavior. We invite researchers to submit original research and review articles on the recent developments in fractional differential equations in anomalous diffusion and thermal conduction and their applications in science, technology, and engineering.

Prof. Dr. Aloisi Somer
Prof. Dr. Ervin K. Lenzi
Guest Editors

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• fractional calculus and fractal media
• thermo-molecular physics
• thermodynamics
• heat and mass transfer
• bio-heat transfer
• fractional thermal conduction
• anomalous thermal diffusion
• nonequilibrium processes
• nonequilibrium thermodynamics
• kinetics theory