Geodesic
A problem in the half-strip for fourth order parabolic equation with time fractional Riemann--Liouville derivative
News of the Kabardin-Balkar scientific center of RAS, no. 5 (2019), pp. 21-29

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In this work a fourth-order inhomogeneous parabolic equation with time fractional derivative is considered. The fractional derivative is understood in the sense of the Riemann–Liouville derivative. The boundary-value problem in the half-strip for equation under consideration is studied. The linearity of the problem allows reducing it to the solution of a homogeneous fourth order parabolic equation with a fractional derivative with respect to the time variable with a homogeneous initial condition and inhomogeneous boundary conditions. In this paper a fundamental solution for fourth-order parabolic equation with time fractional derivative in terms of the Wright function is presented, а representation of the solution of the problem is constructed and uniqueness of the solution in the class of fast growth functions is proved.
Keywords: Riemann–Liouville fractional derivative, fourth order parabolic equation, problem in the half-strip. 
@article{IZKAB_2019_5_a2,
     author = {L. L. Karasheva},
     title = {A problem in the half-strip for fourth order parabolic equation with time fractional {Riemann--Liouville} derivative},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {21--29},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IZKAB_2019_5_a2/}
}
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L. L. Karasheva. A problem in the half-strip for fourth order parabolic equation with time fractional Riemann--Liouville derivative. News of the Kabardin-Balkar scientific center of RAS, no. 5 (2019), pp. 21-29. http://geodesic.mathdoc.fr/item/IZKAB_2019_5_a2/