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This study introduces g-subdiffusion, a novel model for time-evolving media, enabling transitions between diffusion types. It reveals an additional aging process in g-subdiffusion, offering new insights into complex diffusion dynamics.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Materials Science

Background:

  • Subdiffusion describes anomalous transport in complex media.
  • Standard subdiffusion models often assume a static medium structure.
  • Evolving media introduce complexities not captured by traditional models.

Purpose of the Study:

  • To present a novel g-subdiffusion equation using a Caputo fractional time derivative.
  • To model subdiffusion in media with time-evolving structures.
  • To analyze the aging process and transitions between diffusion types.

Main Methods:

  • Application of a subdiffusion equation with a Caputo fractional time derivative with respect to a function g.
  • Mathematical analysis of the g-subdiffusion process and its aging characteristics.
  • Investigation of continuous transitions between subdiffusion and other diffusion types, including ultraslow diffusion.

Main Results:

  • The g-subdiffusion equation effectively models transport in time-evolving media.
  • A continuous transition from subdiffusion to other diffusion types is demonstrated.
  • The g-subdiffusion process introduces an additional aging process beyond standard subdiffusion aging.
  • A method for solving the g-subdiffusion equation is presented.

Conclusions:

  • The g-subdiffusion model provides a flexible framework for studying anomalous transport in dynamic environments.
  • This approach allows for a tunable timescale, facilitating the study of transitions like subdiffusion to ultraslow diffusion.
  • The analysis of the superimposed aging process offers deeper understanding of complex transport phenomena.