**5. Conclusions**

We have studied a nonlinear fractional integro-differential equation involving many finitely Riemann–Liouville fractional integral type nonlinearities together with a non-integral nonlinearity complemented by multi-point sub-strip boundary conditions. In fact, we considered a more general situation by considering the fractional order nonlinear integral terms in the integro-differential equation at hand, which reduce to the usual nonlinear integral terms for *pi* = 1, ∀*i* = 1, ... , *k*. Under appropriate assumptions, the existence and uniqueness results for the given problem are proved by applying the standard tools of the fixed point theory. The results obtained in this paper are not only new, but they also lead to some new results associated with the particular choices of the parameters involved in the problem. For example, our results correspond to the two-strip aperture (*ζ*, *ξ*) boundary value problem when *αj* = 0, ∀*j* = 1, ... , *p*. On the other hand, by letting *γ*1 = 0 = *γ*2 in the the results of this paper, we obtain the ones for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential equation with multi-point boundary conditions. Thus, the work presented in this paper significantly contributes to the existing literature on the topic.

**Author Contributions:** Conceptualization, B.A.; formal analysis, A.A., A.F.A., S.K.N. and B.A.; funding acquisition, A.A.; methodology, A.A., A.F.A., S.K.N. and B.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, funded this project, under gran<sup>t</sup> no. (FP-20-42).

**Acknowledgments:** The Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, funded this project, under gran<sup>t</sup> no. (FP-20-42). The authors, therefore, acknowledge the DSR, with thanks for the technical and financial support provided. The authors thank the reviewers for their constructive remarks on our work.

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