@article{Ouagueni_Arioua_Benhamidouche_2023, title={Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative}, volume={22}, url={https://studmath.up.krakow.pl/article/view/10338}, abstractNote={<p>In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity variable η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e.~Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).</p>}, journal={Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica}, author={Ouagueni, Nora and Arioua, Yacine and Benhamidouche, Noureddine}, year={2023}, month={May}, pages={49–74} }