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 İlhan; Shakirbay G. Kasimov; Shonazar Q. Otaev; Haci Mehmet Baskonus

doi:10.3390/math7030235

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Article

5 March 2019

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

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Department of Mathematics and Science Education, Faculty of Education, Erciyes University, Kayseri 38039, Turkey

Faculty of Mathematics, National University of Uzbekistan, Tashkent 100174, Uzbekistan

Department of Mathematics and Science Education, Faculty of education, Harran University, Sanliurfa 63190, Turkey

Author to whom correspondence should be addressed.

Mathematics2019, 7(3), 235;https://doi.org/10.3390/math7030235

This article belongs to the Special Issue Fractional-Order Integral and Derivative Operators and Their Applications

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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

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