On a nonlinear time-fractional cable equation

Mohamed Jleli; Bessem Samet; Mohamed Jleli; Bessem Samet

doi:10.3934/math.20241146

AIMS Mathematics

2024, Volume 9, Issue 9: 23584-23597. doi: 10.3934/math.20241146

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On a nonlinear time-fractional cable equation

Mohamed Jleli ,
Bessem Samet ^,

Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia; jleli@ksu.edu.sa

Received: 28 April 2024 Revised: 14 June 2024 Accepted: 20 June 2024 Published: 07 August 2024
MSC : 34K37, 35A01, 35B33

A nonlinear time-fractional cable equation posed on the interval $ (0, 1) $ under a homogeneous Dirichlet boundary condition is investigated in this work. The considered equation reflects the anomalous electro-diffusion in nerve cells. Using nonlinear capacity estimates specifically adapted to the considered problem, we establish sufficient conditions for the nonexistence of weak solutions.
- time-fractional cable equation,
- weak solution,
- nonexistence,
- Caputo fractional derivative
Citation: Mohamed Jleli, Bessem Samet. On a nonlinear time-fractional cable equation[J]. AIMS Mathematics, 2024, 9(9): 23584-23597. doi: 10.3934/math.20241146

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Abstract

A nonlinear time-fractional cable equation posed on the interval $ (0, 1) $ under a homogeneous Dirichlet boundary condition is investigated in this work. The considered equation reflects the anomalous electro-diffusion in nerve cells. Using nonlinear capacity estimates specifically adapted to the considered problem, we establish sufficient conditions for the nonexistence of weak solutions.

References

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