**5. Conclusions**

In this paper, we considered questions on the unique solvability of a mixed problem for a partial differential equation of high order with fractional Riemann-Liouville derivatives with respect to time, and with Laplace operators with spatial variables and with nonlocal boundary conditions in Sobolev classes. The solution was found in the form of a series of expansions in eigenfunctions of the Laplace operator with nonlocal boundary conditions. Initial and boundary problems with fractional Riemann-Liouville derivatives with respect to time have many applications [13]. In connection to this, we chose the fractional Riemann-Liouville derivative, although we could consider other types of fractional derivatives.

**Author Contributions:** Methodology, O.A.˙ I.; Resources, S.G.K.; Writing—original draft, S.Q.O.; Writing—review editing, H.M.B.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors gratefully thank the referees for their several suggestions and comments.

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

#### **References**


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