Weakly Coupled Systems of Semi-Linear Fractional <i>σ</i>–Evolution Equations with Different Power Nonlinearities
Seyyid Ali Saiah,
Abdelatif Kainane Mezadek,
Mohamed Kainane Mezadek,
Abdelhamid Mohammed Djaouti,
Ashraf Al-Quran,
Ali M. A. Bany Awad
Affiliations
Seyyid Ali Saiah
Laboratory of Mathematics and Applications, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Hay Essalam, Chlef 02000, Algeria
Abdelatif Kainane Mezadek
Laboratory of Mathematics and Applications, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Hay Essalam, Chlef 02000, Algeria
Mohamed Kainane Mezadek
Laboratory of Mathematics and Applications, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Hay Essalam, Chlef 02000, Algeria
Abdelhamid Mohammed Djaouti
Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia
Ashraf Al-Quran
Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia
Ali M. A. Bany Awad
Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia
The study of small data Sobolev solutions to the Cauchy problem for weakly coupled systems of semi-linear fractional σ–evolution equations with different power nonlinearities is of interest to us in this research. These solutions must exist globally (in time). We explain the relationships between the admissible range of exponents p1 and p2 symmetrically in our main modeland the regularity assumptions for the data by using Lm−Lq estimates of Sobolev solutions to related linear models with a vanishing right-hand side and some fixed point argument. This allows us to prove the global (in time) existence of small data Sobolev solutions.
