Gellerstedt Type Problem for the Loaded Parabolic-Hyperbolic Type Equation with Caputo and Erdelyi-Kober Operators of Fractional Order

被引：6

作者：

Abdullaev, O. Kh. ^{[1
]}

Islomov, B. I. ^{[1
]}

机构：

[1] Natl Univ Uzbekistan, 4 Univ Skaya Str, Tashkent 100174, Uzbekistan

来源：

RUSSIAN MATHEMATICS | 2020年 / 64卷 / 10期

关键词：

loaded equation; parabolic-hyperbolic type; Caputo derivative; Erdelyi-Kober integral operator; integral gluing condition; uniqueness and existence of solution; integral equations;

D O I：

10.3103/S1066369X20100047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The work is devoted to the proof of the uniqueness and existence of solution to local and nonlocal problems with an integral gluing condition for a loaded parabolic-hyperbolic type equation with differential and integral operators of fractional order, in which the trace of the solution appears in the Erdelyi-Kober integral operator. Using the method of energy integrals, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations.

引用

页码：29 / 42

页数：14

共 28 条

[1]

Abdullaev O.Kh, 2019, UZBEK MATH J, V3, P4, DOI [10.29229/uzmj.2019-3-1, DOI 10.29229/UZMJ.2019-3-1]

[2] A NON-LOCAL PROBLEM FOR A LOADED MIXED-TYPE EQUATION WITH A INTEGRAL OPERATOR [J].

Abdullayev, O. Kh. .

VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2016, 20 (02) :220-240

[3]

[Anonymous], 1993, Fractional integral and derivative, theory and applications

[4]

[Anonymous], 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations

[5] Solvability of an elliptic partial differential equation with boundary condition involving fractional derivatives [J].

Berdyshev, A. S. ;

Kadirkulov, B. J. ;

Nieto, J. J. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2014, 59 (05) :680-692

[6] On a non-local boundary problem for a parabolic-hyperbolic equation involving a Riemann-Liouville fractional differential operator [J].

Berdyshev, A. S. ;

Cabada, A. ;

Karimov, E. T. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (06) :3268-3273

[7]

Diethelm K., 1999, Scientific Computing in Chemical Engineering, VII, P217

[8]

GLOCKLE WG, 1995, BIOPHYS J, V68, P46, DOI 10.1016/S0006-3495(95)80157-8

[9]

Hilfer R., 2000, APPL FRACTIONAL CALC

[10]

Kilbas A, 2006, THEORY APPL FRACTION

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