Abstract:
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.
Keywords:
fractional calculus, Riemann–Liouville integral-differential operator, differential equations with partial fractional derivatives, parabolic equation, 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.
Original article submitted 05/XI/2015 revision submitted – 07/II/2016
Citation:
F. G. Khushtova, “Cauchy problem for a parabolic equation with Bessel operator and Riemann–Liouville partial derivative”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:1 (2016), 74–84
\Bibitem{Khu16}
\by F.~G.~Khushtova
\paper Cauchy problem for a parabolic equation with Bessel operator and Riemann--Liouville partial derivative
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2016
\vol 20
\issue 1
\pages 74--84
\mathnet{http://mi.mathnet.ru/vsgtu1455}
\crossref{https://doi.org/10.14498/vsgtu1455}
\zmath{https://zbmath.org/?q=an:06964474}
\elib{https://elibrary.ru/item.asp?id=26898117}
Linking options:
https://www.mathnet.ru/eng/vsgtu1455
https://www.mathnet.ru/eng/vsgtu/v220/i1/p74
This publication is cited in the following 3 articles:
F. G. Khushtova, “Pervaya kraevaya zadacha v pryamougolnoi oblasti dlya differentsialnogo uravneniya s operatorom Besselya i chastnoi proizvodnoi Rimana–Liuvillya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 25:2 (2021), 241–256
F. G. Khushtova, “Vtoraya kraevaya zadacha v polupolose dlya B-parabolicheskogo uravneniya s proizvodnoi Gerasimova-Kaputo po vremeni”, Vestnik KRAUNTs. Fiz.-mat. nauki, 33:4 (2020), 37–50
F. G. Khushtova, “K probleme edinstvennosti resheniya zadachi Koshi dlya uravneniya drobnoi diffuzii s operatorom Besselya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 774–784
Citation in format AMSBIB
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