In this paper, we first investigate the monotonicity and limit problem of fractional integral functions. We prove that fractional integral function is a monotone function, and the limit of fractional integral function exists as \(t\rightarrow +\infty \) . Using the fixed point theorem together with new results on fractional integral functions, we show that Riemann-Liouville fractional differential equations have at least one nonincreasing solution in \(C_{1-\beta }^{+}(0,+\infty )\) . The asymptotic behavior of solutions is also discussed in different conditions. One novelty in this paper is that we investigate the asymptotic behavior of solutions of Riemann-Liouville fractional differential equations by using the monotonicity of functions. We prove that the solution is a nonincreasing function and converges to a constant. We also discuss the asymptotic behavior of solutions of fractional differential equations without the monotonicity assumption. Finally, several examples are given to illustrate our main results.
