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

Yıl 2022, , 287 - 299, 30.09.2022

Rabah Djemiat Bilal Bastı , Noureddine Benhamidouche

https://doi.org/10.31197/atnaa.1031436

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

• Y. Arioua, B. Basti and N. Benhamidouche, Initial value problem for nonlinear implicit fractional differential equations with Katugampola derivative, Appl. Math. E-Notes, 19 (2019), 397--412.
• 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.
• 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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• N. Benhamidouche, Exact solutions to some nonlinear PDEs, travelling profiles method, Electronic Journal of Qualitative Theory of Differential Equation 15 (2008), 1--7.
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