**6. Conclusions**

The main aim of the paper is to sugges<sup>t</sup> a scheme for the approximate solving of the initial value problem for scalar nonlinear Riemann-Liouville fractional differential equations with a constant delay on a finite interval. The iterative scheme is based on the method of lower and upper solutions. In connection with this, mild lower and mild upper solutions are defined. An algorithm for constructing two monotone sequences of mild lower and mild upper solutions, respectively, is given. It is proved both sequences are convergen<sup>t</sup> to the exact solution of the studied problem. The iterative scheme is used in a computer environment to illustrate its application for solving a particular nonlinear problem. The suggested and computerized algorithm can be applied to solve approximately and to study the behavior of scalar models with RL fractional derives and delays. The practical application requires the next step in the investigations, more exactly to obtain an algorithm for approximate solving of systems with RL derivatives and delays.

**Author Contributions:** Conceptualization, S.H.; Methodology, S.H.; Software, A.G. and K.S.; Validation, A.G. and K.S.; Formal Analysis, S.H.; Writing—Original Draft Preparation, S.H., A.G. and K.S.; Writing—Review and Editing, S.H., A.G. and K.S.; Visualization, A.G. and K.S.; Supervision, S.H.; Funding Acquisition, S.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** S.H. is partially supported by the Bulgarian National Science Fund under Project KP-06-N32/7. **Conflicts of Interest:** The authors declare no conflict of interest.
