Electron. J. Differential Equations, Vol. 2020 (2020), No. 111, pp. 1-14.

Convergence of solutions of fractional differential equations to power-type functions

Mohammed Dahan Kassim, Nasser Eddine Tatar

In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some existing well-known results on solutions of ordinary differential equations. Appropriate estimations and lemmas such as a fractional version of L'Hopital's rule are used.

Submitted September 15, 2020. Published November 4, 2020.
Math Subject Classifications: 34E10, 26A33, 34A08.
Key Words: Asymptotic behavior; boundedness; fractional differential equation; Caputo fractional derivative; Riemann-Liouville fractional derivative.

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Mohammed Dahan Kassim
Department of Basic Engineering Sciences
College of Engineering
Imam Abdulrahman Bin Faisal University, P.O. Box 1982
Dammam 31441, Saudi Arabia
email: mdkassim@iau.edu.sa
Nasser Eddine Tatar
King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran, 31261, Saudi Arabia
email: tatarn@kfupm.edu.sa

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