TY - JOUR
AU - Ouagueni, Nora
AU - Arioua, Yacine
AU - Benhamidouche, Noureddine
PY - 2023/05/29
Y2 - 2023/12/05
TI - Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 22
IS -
SE - Published
DO -
UR - https://studmath.up.krakow.pl/article/view/10338
SP - 49-74
AB - <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>
ER -