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Research Article | Open Access

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
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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.

Keywords

time-fractional cable equationweak solutionnonexistenceCaputo fractional derivative
CLC number: 34K37, 35A01, 35B33

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 23584-23597
DOI: 10.3934/math.20241146

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Jleli M, Samet B. On a nonlinear time-fractional cable equation. AIMS Mathematics, 2024, 9(9): 23584-23597. https://doi.org/10.3934/math.20241146

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Received: 28 April 2024
Revised: 14 June 2024
Accepted: 20 June 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)