**5. Conclusions**

In previous sections, we have presented the existence and uniqueness of extremal solutions to a Cauchy problem with *ψ*-Caputo fractional derivative. Moreover, some uniqueness results are obtained. The proof of the existence results is based on the monotone iterative technique combined with the method of upper and lower solutions. Moreover, an example is presented to illustrate the validity of our main results. Our results are not only new in the given configuration but also correspond to some new situations associated with the specific values of the parameters involved in the given problem.

**Author Contributions:** conceptualization, C.D., Z.B., M.B. and A.C.; methodology, C.D., Z.B., M.B. and A.C.; formal analysis, C.D., Z.B., M.B. and A.C.; investigation, C.D., Z.B., M.B. and A.C.; writing—original draft preparation, C.D., Z.B., M.B. and A.C.; writing—review and editing, C.D., Z.B., M.B. and A.C.; funding acquisition, A.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** The fourth author is supported by the Agencia Estatal de Investigación (AEI) of Spain under gran<sup>t</sup> MTM2016-75140-P, co-financed by the European Community fund FEDER. The fourth author is also supported by Xunta de Galicia, project ED431C 2019/02 (Spain).

**Conflicts of Interest:** The authors declare no conflict of interest.
