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

Abstract

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.

Keywords

• asymptotic behavior
• boundedness
• fractional differential equation
• caputo fractional derivative
• riemann-liouville fractional derivative