Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order

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Original research article

Author(s):

Rabah Djemiat^a, Bilal Basti^b, Noureddine Benhamidouche^a

^a Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University of M’sila, M’sila, Algeria.
^b Department of Mathematics, Ziane Achour University of Djelfa, Djelfa, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 6(3), 287-299.

Received: December 2, 2021

Accepted: March 6, 2022

Published: March 10, 2022

Abstract

This paper particularly addresses and discusses some analytical studies on the existence and uniqueness of global or blow-up solutions under the traveling profile forms for a free boundary problem of two-dimensional diffusion equations of moving fractional order. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.

Keywords: Fractional diffusion, Moving fractional order, Free boundary, Blow-up, Global existence, Uniqueness.

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APA Style

Djemiat, R., Bastı, B., & Benhamidouche, N. (2022). Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order. Advances in the Theory of Nonlinear Analysis and its Application, 6(3), 287-299.