Abstract
The asymptotic behavior, the decay and the boundedness of solutions are discussed for the system of fractional differential equations including two types of fractional derivatives the Caputo fractional derivative (CFD) and the Riemann-Liouville fractional derivative (RLFD). Reasonable sufficient conditions are determined ensuring that solutions for the system with nonlinear right hand sides approach a power type function, power type decay and boundedness as time goes to infinity. Our approach is based on appropriate desingularization techniques and generalized the inequality of the Gronwall-Bellman. Convenient assessments and lemmas such as a fractional version of L’Hopital’s rule are used.
| Original language | English |
|---|---|
| Pages (from-to) | 145-166 |
| Number of pages | 22 |
| Journal | Progress in Fractional Differentiation and Applications |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2023 |
Bibliographical note
Funding Information:Acknowledgement. We are thankful to the reviewers for their careful reading and suggestions. The second author is very grateful to King Fahd University of Petroleum and Minerals for its financial support through project No.SB201006.
Publisher Copyright:
© 2023 NSP Natural Sciences Publishing Cor.
Keywords
- Asymptotic behavior
- boundedness
- desingularization technique
- fractional differential equation
- power type decay
- Riemann-Liouville and Caputo fractional derivatives
- weighted space
ASJC Scopus subject areas
- Analysis
- Applied Mathematics