An Initial Value Problem Involving Caputo-Hadamard Fractional Derivative: The Extremal Solutions and Stabilization

Abstract

In this paper, the existence of extremal solutions of Caputo-Hadamard-type fractional differential equations (CHFDEs) with order $\alpha \in (1,2)$ is established by employing the method of lower and upper solutions. Moreover, sufficient condition that ensures the stability of a class of CHFDE is also provided. Some examples are given to illustrate our main results.

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