A single quenching point for a fractional heat equation based on the Riemann-Liouville fractional derivative with a nonlinear concentrate source

Abstract

Abstract This paper aims to study the quenching problem in a fractional heat equation with the Riemann-Liouville fractional derivative. The existence and uniqueness of a solution for the problem are obtained by transforming the problem to an equivalent integral equation. The condition for the quenching occurrence in a finite time is given. Furthermore, the quenching point set is shown.

Keywords

• quenching
• fractional heat equation
• Riemann-Liouville derivative
• existence and uniqueness