Analysis of Heat Conduction and Anomalous Diffusion in Fractional Calculus

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 May 2024 | Viewed by 205

Special Issue Editors

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Guest Editor
Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil
Interests: fractional differential operators; fractional dual-phase-lag heat conduction theory; spatial and time fractional derivative; fractional diffusion; anomalous heat diffusion; heat conduction

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Guest Editor
Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil
Interests: anomalous diffusion; liquid crystals; impedance; fractional dynamics; nonextensive thermostatistics
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Special Issue Information

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

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • 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

Published Papers

This special issue is now open for submission.
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