Asymptotic power type behavior of solutions to a nonlinear fractional integro-differential equation

Abstract

This article concerns a general fractional differential equation of order between 1 and 2. We consider the cases where the nonlinear term contains or does not contain other (lower order) fractional derivatives (of Riemann-Liouville type). Moreover, the nonlinearity involves also a nonlinear non-local in time term. The case where this non-local term has a singular kernel is treated as well. It is proved, in all these situations, that solutions approach power type functions at infinity.

Keywords

• Asymptotic behavior
• fractional integro-differential equation
• Riemann-Liouville fractional derivative
• nonlocal source
• integral inequalities