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

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.

The quenching of solutions to time–space fractional Kawarada problems

“…In this section we show that the local in time solution to (1.1) cannot always be extended to a global in time solution. This fact is well established in the cases for α = s = 1 and also recently for s = 1 and Ω = [0, 1] ⊂ R [9,8,11,12,21]. We now show that this result holds in a similar manner for any α, s ∈ (0, 1).…”

Riemann zeta fractional derivative—functional equation and link with primes

“…Fractional calculus has recently been applied to the theory of meromorphic functions (see, e.g., [8][9][10][11]). In particular, the α-order fractional derivative of the Riemann ζ function given by ζ (α)…”