Global Existence of Small Data Solutions to Weakly Coupled Systems of Semi-Linear Fractional σ–Evolution Equations with Mass and Different Nonlinear Memory terms-Reference-Cited by-同舟云学术

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

Published:2024-06-22 Issue:13 Volume:12 Page:1942
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Saiah Seyyid Ali¹^ORCID,Kainane Mezadek Abdelatif¹^ORCID,Kainane Mezadek Mohamed¹^ORCID,Mohammed Djaouti Abdelhamid²³^ORCID,Al-Quran Ashraf²³^ORCID,Bany Awad Ali M. A.⁴

Affiliation:

1. Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria

2. Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia

3. Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia

4. Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia

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 Lp−Lq 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 (p1,p2,…,pk).

Funder

Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/13/1942/pdf

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