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

Authors : Rabah DJEMİAT, Bilal BASTI, Noureddine BENHAMİDOUCHE

Pages : 287-299

Doi:10.31197/atnaa.1031436

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Publication Date : 2022-09-30

Article Type : Research Paper

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