Geodesic
First Boundary-Value Problem in the Half-Strip for a Parabolic-Type Equation with Bessel Operator and Riemann--Liouville Derivative
Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 921-928

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The first boundary-value problem in the half-strip for a parabolic-type equation with Bessel operator and Riemann–Liouville derivative is studied. In the case of the zero initial condition, the representation of the solution in terms of the Fox $H$-function is obtained. The uniqueness of the solution for a class of functions vanishing at infinity is proved. It is shown that when the equation under consideration coincides with the Fourier equation, the obtained representation of the solution becomes the known representation of the solution of the corresponding problem.
Mots-clés : parabolic-type equation, Fourier equation, diffusion of fractional order.
Keywords: first boundary-value problem, Fox $H$-function, Riemann–Liouville derivative, Bessel operator 
@article{MZM_2016_99_6_a10,
     author = {F. G. Khushtova},
     title = {First {Boundary-Value} {Problem} in the {Half-Strip} for a {Parabolic-Type} {Equation} with {Bessel} {Operator} and {Riemann--Liouville} {Derivative}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {921--928},
     publisher = {mathdoc},
     volume = {99},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a10/}
}
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F. G. Khushtova. First Boundary-Value Problem in the Half-Strip for a Parabolic-Type Equation with Bessel Operator and Riemann--Liouville Derivative. Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 921-928. http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a10/