BOUNDEDNESS, MONOTONICITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

By the Schauder fixed point theorem, we first investigate the boundedness and monotonicity of solutions of Caputo fractional differential equations. We also study the asymptotic behavior of solutions of Caputo fractional differential equations under some different conditions. We prove that the solutions of the Caputo fractional differential equations converge asymptotically to a constant as $t\to +\infty$. Finally, several examples are given to illustrate our main results.