Solvability of the boundary-value problem for a mixed equation involving hyper-Bessel fractional differential operator and bi-ordinal Hilfer fractional derivative

被引：10

作者：

Karimov, Erkinjon ^{[1
,2
]}

Ruzhansky, Michael ^{[3
,4
]}

Toshtemirov, Bakhodrijon ^{[1
,3
]}

机构：

[1] Acad Sci Uzbek, VI Romanovskiy Inst Math, Tashkent, Uzbekistan

[2] Fergana State Univ, Dept Math Anal & Differential Equat, Fergana, Uzbekistan

[3] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium

[4] Queen Mary Univ London, Sch Math Sci, London, England

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 01期

关键词：

bi-ordinal Hilfer's derivative; boundary-value problems; fractional wave equation; hyper-Bessel fractional differential operator; sub-diffusion equation; DIFFUSION EQUATION; NONLOCAL PROBLEM; RELAXATION; EVOLUTION; MODEL;

D O I：

10.1002/mma.8491

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a rectangular domain, a boundary-value problem is considered for a mixed equation with a regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. By using the method of separation of variables a unique solvability of the considered problem has been established. Moreover, we have found the explicit solution of initial-boundary problems for the heat equation with the regularized Caputo-like counterpart of the hyper-Bessel differential operator with the non-zero starting point.

引用

页码：54 / 70

页数：17

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