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

Öz

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.

Anahtar Kelimeler

• Fractional diffusion
• moving fractional order
• free boundary
• blow-up
• global existence
• uniqueness

Kaynakça

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2. B. Basti, Y. Arioua and N. Benhamidouche, Existence and uniqueness of solutions for nonlinear Katugampola fractional differential equations, J. of Math. and Applications, 42 (2019), 35--61.
3. B. Basti, Y. Arioua and N. Benhamidouche, Existence results for nonlinear Katugampola fractional differential equations with an integral condition, Acta Mathematica Universitatis Comenianae, 89 (2020), 243--260.
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