Abstract
In this paper we study Fourier problem for a fractional diffusion-wave equation with the Riemann–Liouville derivative. The correctness of the problem for the fractional diffusion–wave equation with necessary nonlocal conditions is established, and its solution in terms of the Green’s function is constructed.
REFERENCES
A. V. Pskhu, Partial Differential Equations of Fractional Order (Nauka, Moscow, 2005) [in Russian].
M. O. Mamchuev, Boundary Problems for Partial Differential Equations and Systems of Equations of Fractional Order (KBNTs RAN, Nal’chik, 2013) [in Russian].
E. G. Bazhlekova, ‘‘Duhamel-type representations of the solutions of non-local boundary value problems for the fractional diffusion-wave equation,’’ in Transform Methods and Special Functions, Proceedings of 2nd International Workshop, Varna, August 23–30, 1996.
Z. A. Nakhusheva, ‘‘A modified Samarskiy problem for a nonlocal diffusion equation,’’ Dokl. Adyg. (Cherkess.) Mezhdun. Akad. Nauk 2 (2), 36–41 (1997).
M. O. Mamchuev, ‘‘Necessary nonlocal conditions and the Samarskiy problem for the diffusion-wave equation,’’ Dokl. Adyg. (Cherkess.) Mezhdun. Akad. Nauk 9 (2), 16–19 (2007).
M. O. Mamchuev, ‘‘Necessary nonlocal conditions for the diffusion-wave equation,’’ Vestn. Samar. Univ., Estestvennonauch. Ser. 7 (118), 45–60 (2014).
F. M. Losanova, ‘‘On a nonlocal boundary problem for loaded equation of the parabolic type,’’ Dokl. Adyg. (Cherkess.) Mezhdun. Akad. Nauk 9 (2), 54–58 (2007).
M. O. Mamchuev, ‘‘Solvability of a nonlocal boundary problem for the diffusion-wave equation,’’ Dokl. Adyg. (Cherkess.) Mezhdun. Akad. Nauk 10 (1), 32–34 (2008).
M. O. Mamchuev, ‘‘On the well-posedness of boundary value problems for a fractional diffusion-wave equation and one approach to solving them,’’ Differ. Equat. 56, 756–760 (2020).
A. M. Nakhushev, Fractional Calculus and Its Application (Fizmatlit, Moscow, 2003) [in Russian].
S. Kh. Gekkieva, ‘‘The Cauchy problem for a generalized transfer equation with a fractional time-derivative,’’ Dokl. Adyg. (Cherkess.) Mezhdun. Akad. Nauk 5 (1), 16–19 (2000).
E. M. Wright, ‘‘On the coefficients of power series having exponential singularities,’’ J. London Math. Soc. 8 (29), 71–79 (1933).
A. M. Nakhushev, Problems with a Shift for Partial Differential Equations (Nauka, Moscow, 2006) [in Russian].
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by T. K. Yuldashev)
Rights and permissions
About this article
Cite this article
Mamchuev, M.O., Mamchuev, A.M. Fourier Problem for Fractional Diffusion–Wave Equation. Lobachevskii J Math 44, 620–628 (2023). https://doi.org/10.1134/S1995080223020257
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080223020257