Axioms (Sep 2024)

A Two-Dimensional Nonlocal Fractional Parabolic Initial Boundary Value Problem

  • Said Mesloub,
  • Eman Alhazzani,
  • Hassan Eltayeb Gadain

DOI
https://doi.org/10.3390/axioms13090646
Journal volume & issue
Vol. 13, no. 9
p. 646

Abstract

Read online

In this paper, we investigate a two-dimensional singular fractional-order parabolic partial differential equation in the Caputo sense. The partial differential equation is supplemented with Dirichlet and weighted integral boundary conditions. By employing a functional analysis method based on operator theory techniques, we prove the existence and uniqueness of the solution to the posed nonlocal initial boundary value problem. More precisely, we establish an a priori bound for the solution from which we deduce the uniqueness of the solution. For proof of its existence, we use various density arguments.

Keywords