Geodesic
Cauchy problem for a parabolic equation with Bessel operator and Riemann--Liouville partial derivative
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 74-84

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In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.
Mots-clés : fractional calculus, parabolic equation
Keywords: Riemann–Liouville integral-differential operator, differential equations with partial fractional derivatives, Bessel operator, the modified Bessel function of the first kind, Wright function, the integral transform with Wright function in the kernel, Fox $H$-function, Cauchy problem, Tikhonov condition. 
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     author = {F. G. Khushtova},
     title = {Cauchy problem for a parabolic equation with {Bessel} operator and {Riemann--Liouville} partial derivative},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {74--84},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2016_20_1_a6/}
}
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F. G. Khushtova. Cauchy problem for a parabolic equation with Bessel operator and Riemann--Liouville partial derivative. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 74-84. http://geodesic.mathdoc.fr/item/VSGTU_2016_20_1_a6/