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Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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Abstract

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equations) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern mechanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

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  1. Institute of Applied Mathematics, School of Math & System Science, Shandong University, Jinan, 250100, China

    Xu Mingyu

  2. State Key Laboratory of Turbulence and Complex Systems & Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, China

    Tan Wenchang

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Xu, M., Tan, W. Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics. SCI CHINA SER G 49, 257–272 (2006). https://doi.org/10.1007/s11433-006-0257-2

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