Electron. J. Differential Equations, Vol. 2018 (2018), No. 90, pp. 1-10.

Well-posed problems for the fractional Laplace equation with integral boundary conditions

Niyaz Tokmagambetov, Berikbol T. Torebek

In this remark we study the boundary-value problems for a fractional analogue of the Laplace equation with integral boundary conditions in rectangular and half-strip domains. We prove the existence and uniqueness of solutions by using the spectral decomposition method.

Submitted February 8, 2018. Published April 12, 2018.
Math Subject Classifications: 35R30, 35K05, 35K20.
Key Words: Caputo operator; Riemann-Liouville operator; fractional Laplace; Mittag-Leffler function; self-adjoint operator; boundary value problem.

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  Niyaz Tokmagambetov
Al-Farabi Kazakh National University
050040, Al-Farabi ave., 71
Almaty, Kazakhstan
email: tokmagambetov@math.kz
Berikbol T. Torebek
Institute of Mathematics and Mathematical Modeling
050010, Pushkin st., 125
Almaty, Kazakhstan
email: torebek@math.kz

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