Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations
In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.
KeywordsAsymptotic behavior fractional integro-differential equation Caputo fractional derivative integral inequalities nonlocal source
Mathematics Subject Classification34A08 35B40 26D10
The authors would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals (KFUPM) through project number IN161010.
- 5.Alsaedi, A.: Existence of solutions for integrodifferential equations of fractional order with antiperiodic boundary conditions. Int. J. Differ. Equ. 2009 (2009)Google Scholar
- 26.Mustafa, O.G., Baleanu, D.: On the Asymptotic Integration of a Class of Sublinear Fractional Differential Equations. arXiv:0904.1495 (2009) (arXiv preprint)