Existence of solutions for a class of fractional dynamical systems with two damping terms in Banach space

Abstract

This paper studies the existence of solutions for fractional dynamical systems with two damping terms in Banach space. First, we generalize the well-known Gronwall inequality. Next, according to fixed-point theorems and inequalities, the existence results for the considered system are obtained. At last, an example is used to support the main results.

Keywords

• gronwall inequality
• fixed point theorems
• fractional differential equation
• two damping terms