Monotonicity and asymptotic behavior of solutions for Riemann-Liouville fractional differential equation

2023/08/29 by Tao Zhu, Zhu, Tao
Mathematics · #Nonlinear Differential Equations Analysis #Fractional Differential Equations Solutions #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2308.15036

Abstract

In this paper, we first investigate the monotonicity and limit problem of the fractional integral functions. By fixed point theorem and these new results of the fractional integral functions, we present that the Riemann-Liouville fractional differential equations has at least one decreasing solution in C_1-β⁺(0,+∞). The asymptotic behavior of solutions is also discussed under some different conditions. The novelty in this paper is that we investigate the asymptotic behavior of Riemann-Liouville fractional differential equations by the monotonicity of functions. Finally, several examples are given to illustrate our main results.

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