"Asymptotic Behavior for Fractional Systems with Lower-Order Fractional" by Mohammed D. Kassim and Nasser-Eddine Tatar

Progress in Fractional Differentiation & Applications

Article Title

Asymptotic Behavior for Fractional Systems with Lower-Order Fractional Derivatives

Authors

Mohammed D. Kassim, Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi ArabiaFollow
Nasser-Eddine Tatar, Department of Mathematics, King Fahd University of Petroleum and Minerals, Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, Dhahran 31261, Saudi ArabiaFollow

Author Country (or Countries)

Saudi Arabia

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090111

Recommended Citation

D. Kassim, Mohammed and Tatar, Nasser-Eddine (2023) "Asymptotic Behavior for Fractional Systems with Lower-Order Fractional Derivatives," Progress in Fractional Differentiation & Applications: Vol. 9: Iss. 1, Article 11.
DOI: http://dx.doi.org/10.18576/pfda/090111
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol9/iss1/11

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