Work

A Two-Dimensional Nonlocal Fractional Parabolic Initial Boundary Value Problem

Year: 2024

Type: article

Abstract: 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.

Source: Axioms

DOI: 10.3390/axioms13090646

Authors: Said Mesloub, Eman Alhazzani, Hassan Eltayeb Gadain

Institution: King Saud University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: King Saud University