Blow-up results of a time fractional heat equation with a nonlinear Neumann boundary condition

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Published: Jan 20, 2026
DOI: https://doi.org/10.5556/j.tkjm.57.2026.5910
Keywords:
Fractional heat equation, blow up, nonlinear boundary condition, maximum principles

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Hind Ghazi Hameed
Department of Mathematics, College of Education, Tikrit University
Burhan Selcuk
https://orcid.org/0000-0002-5141-5148
Maan A. Rasheed
Department of Mathematics, College of Science for Women, University of Baghdad, Iraq

Abstract

The study of blow-up problems for time Caputo fractional heat equations are of great wide-ranging interest for its multitude of applications and the fact that these kinds of problems are found in several areas of science and engineering. This article is concerned with the blow-up solutions of a time fractional heat equation subject to a nonlinear Neumann boundary condition of power type. Firstly, under some restricted conditions, it is proved that every positive solution blows up in finite time. Secondly, it is proved that the blow up phenomenon can only occurs at the boundary.

Article Details

How to Cite
Hameed, H. G., Selcuk, B., & Rasheed, M. A. (2026). Blow-up results of a time fractional heat equation with a nonlinear Neumann boundary condition. Tamkang Journal of Mathematics, 57(1), 51–62. https://doi.org/10.5556/j.tkjm.57.2026.5910
Issue
Vol. 57 No. 1 (2026)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biographies

Hind Ghazi Hameed, Department of Mathematics, College of Education, Tikrit University

Department of Mathematics, College of Education, Tikrit University

Burhan Selcuk

Assist. Prof. Dr. / Computer Engineering Department

Maan A. Rasheed, Department of Mathematics, College of Science for Women, University of Baghdad, Iraq

Department of Mathematics, College of Science for Women, University of Baghdad, Iraq

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