**On the Solvability of a Mixed Problem for a High-Order Partial Differential Equation with Fractional Derivatives with Respect to Time, with Laplace Operators with Spatial Variables and Nonlocal Boundary Conditions in Sobolev Classes**

#### **Onur Alp ˙ Ilhan 1,\*, Shakirbay G. Kasimov 2, Shonazar Q. Otaev <sup>2</sup> and Haci Mehmet Baskonus <sup>3</sup>**


Received: 16 November 2018; Accepted: 1 March 2019; Published: 5 March 2019

**Abstract:** In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes.

**Keywords:** Banach space; Sobolev space; Laplace operators; nonlocal boundary conditions.

**MSC:** 35M12; 46B25; 46E39
