Existence and uniqueness for a mixed fractional differential system with slit-strips conditions (Q6640244)

In this paper, the authors study the existence and uniqueness of solutions of systems of Caputo fractional differential equations with continuous nonlinearities by applying some known fixed-point theorems. Some examples are provided.\N\N\textbf{Reviewer's remark}: The following reference [\textit{K. Q. Lan}, ``Equivalences of nonlinear higher order fractional differential equations with integral equations'', Math. Methods Appl. Sci. (to appear)] shows that the continuity of nonlinearities is not sufficient for solutions of integral equations which are the solutions of higher order Caputo fractional equations. Remark 13 in the reference [\textit{K. Lan} and \textit{J. R. L. Webb}, Fract. Calc. Appl. Anal. 26, No. 3, 962--988 (2023; Zbl 1522.34025)] shows that one can not prove so far that solutions of integral equations are the solutions of the first order Caputo fractional equations even when the nonlinearities are sufficiently smooth.