Existence and uniqueness for a mixed fractional differential system with slit-strips conditions
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.
scientific article; zbMATH DE number 7946143