Global solutions for time-space fractional fully parabolic Keller–Segel system

  • Aruchamy Akilandeeswari

    Anna University, Chennai, India
  • Somnath Gandal

    Indian Institute of Technology Gandhinagar, Gandhinagar, India
  • Jagmohan Tyagi

    Indian Institute of Technology Gandhinagar, Gandhinagar, India
Global solutions for time-space fractional fully parabolic Keller–Segel system cover
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Abstract

We show the existence of a global solution to time-space fractional fully parabolic Keller–Segel system:

under the smallness condition on the initial data, where , and , and denote the cell density and the concentration of the chemoattractant, respectively, and denotes the Caputo fractional derivative of order with respect to time . The nonlocal operator , defined with respect to the space variable , is known as the Laplacian of order . We establish the existence of weak solution to the above system by fixed-point arguments under suitable conditions on and .

Cite this article

Aruchamy Akilandeeswari, Somnath Gandal, Jagmohan Tyagi, Global solutions for time-space fractional fully parabolic Keller–Segel system. Z. Anal. Anwend. (2024), published online first

DOI 10.4171/ZAA/1776