Global Existence of Small Data Solutions to Weakly Coupled Systems of Semi-Linear Fractional σ –Evolution Equations with Mass and Different Nonlinear Memory terms

Seyyid Ali Saiah, Abdelatif Kainane Mezadek (), Mohamed Kainane Mezadek, Abdelhamid Mohammed Djaouti (), Ashraf Al-Quran and Ali M. A. Bany Awad
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Seyyid Ali Saiah: Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria
Abdelatif Kainane Mezadek: Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria
Mohamed Kainane Mezadek: Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria
Abdelhamid Mohammed Djaouti: Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia
Ashraf Al-Quran: Preparatory Year, 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

Mathematics, 2024, vol. 12, issue 13, 1-20

Abstract: We study in this paper the long-term existence of solutions to the system of weakly coupled equations with fractional evolution and various nonlinearities. Our objective is to determine the connection between the regularity assumptions on the initial data, the memory terms, and the permissible range of exponents in a specific equation. Using L p − L q estimates for solutions to the corresponding linear fractional σ –evolution equations with vanishing right-hand sides, and applying a fixed-point argument, the existence of small data solutions is established for some admissible range of powers ( p 1 , p 2 , … , p k ) .

Keywords: ? –evolution equations; small data solutions; global in time existence; fractional equations; nonlinear memory; weakly coupled system; loss of decay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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