Cauchy problem for a loaded hyperbolic equation with the Bessel operator

被引：0

作者：

Baltaeva, Umida ^{[1
,2
,3
,4
]}

Khasanov, Bobur ^{[1
]}

机构：

[1] Uzbek Acad Sci, Khorezm Mamun Acad, Dept Exact Sci, Tashkent, Uzbekistan

[2] Urgench State Univ, Dept Appl Math, Urgench, Uzbekistan

[3] Inst Math, Tashkent, Uzbekistan

[4] Univ Potsdam, Potsdam, Germany

来源：

MATHEMATICA SLOVACA | 2024年 / 74卷 / 05期

关键词：

Cauchy problem; hyperbolic equations; loaded equation; Bessel operator; transmutation operator; Erd & eacute; lyi-Kober operator; ERDELYI-KOBER OPERATOR; DIFFERENTIAL-EQUATIONS;

D O I：

10.1515/ms-2024-0090

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work is devoted to the study of the Cauchy problem for a loaded differential equation with the Bessel operator. When studying problems for loaded equations, the properties of Erd & eacute;lyi-Kober operators are used as transformation operators concerning a relation. We obtain an explicit form of the solution to the Cauchy problem for a loaded one-dimensional differential equation. At the end of the work, we will show several examples on graphs.

引用

页码：1241 / 1254

页数：14

共 33 条

[1] Solvability of the boundary-value problem for a linear loaded integro-differential equation in an infinite three-dimensional domain [J].

Agarwal, Praveen ;

Baltaeva, Umida ;

Alikulov, Yolqin .

CHAOS SOLITONS & FRACTALS, 2020, 140

[2] Cauchy problem for a high-order loaded integro-differential equation [J].

Baltaeva, Umida ;

Baltaeva, Iroda ;

Agarwal, Praveen .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (13) :8115-8124

[3]

Bitsadze A.V., 1988, Gordon and Breach Science

[4]

Carroll R. W., 1976, SINGULAR DEGENERATE

[5]

Chen GQG, 2010, CONTEMP MATH, V526, P53

[6] The transmutation operator method for efficient solution of the inverse Sturm-Liouville problem on a half-line [J].

Delgado, Briceyda B. ;

Khmelnytskaya, Kira, V ;

Kravchenko, Vladislav V. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (18) :7359-7366

[7] Solvability of Degenerating Hyperbolic Differential Equations with Unbounded Operator Coefficients [J].

Glushak, A., V .

DIFFERENTIAL EQUATIONS, 2021, 57 (01) :60-74

[8] Degenerate parabolic stochastic partial differential equations [J].

Hofmanova, Martina .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (12) :4294-4336

[9]

Karimov S., 2023, Bol. Soc. Mat. Mex, V29

[10] Method of solving the Cauchy problem for one-dimensional polywave equation with singular Bessel operator [J].

Karimov S.T. .

Russian Mathematics, 2017, 61 (8) :22-35

← 1 2 3 4 →