Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance
We study the Tricomi problem for the functional-differential mixed-compound equation $LQu(x,y)=0$ in the class of twice continuously differentiable solutions. Here $L$ is a differential-difference operator of mixed parabolic-elliptic type with Riemann–Liouville fractional derivative and linear shift...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Samara State Technical University
2019-12-01
|
| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/34678/23027 |
| _version_ | 1818059804163178496 |
|---|---|
| author | Alexandr Nikolaevich Zarubin Elena Viktorovna Chaplygina |
| author_facet | Alexandr Nikolaevich Zarubin Elena Viktorovna Chaplygina |
| author_sort | Alexandr Nikolaevich Zarubin |
| collection | DOAJ |
| description | We study the Tricomi problem for the functional-differential mixed-compound equation $LQu(x,y)=0$ in the class of twice continuously differentiable solutions. Here $L$ is a differential-difference operator of mixed parabolic-elliptic type with Riemann–Liouville fractional derivative and linear shift by $y$. The $Q$ operator includes multiple functional delays and advances $a_1(x)$ and $a_2(x)$ by $x$. The functional shifts $a_1(x)$ and $a_2(x)$ are the orientation preserving mutually inverse diffeomorphisms. The integration domain is $D=D^+\cup D^-\cup I$. The “parabolicity” domain $D^+$ is the set of $(x,y)$ such that $x_0 |
| first_indexed | 2024-12-10T13:22:20Z |
| format | Article |
| id | doaj.art-cd04e4746e304cc6b3dff004757413bb |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:22:20Z |
| publishDate | 2019-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-cd04e4746e304cc6b3dff004757413bb2022-12-22T01:47:17ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812019-12-01231203610.14498/vsgtu164831191Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advanceAlexandr Nikolaevich Zarubin0Elena Viktorovna Chaplygina1Orel State University named after I. S. TurgenevOrel State University named after I. S. TurgenevWe study the Tricomi problem for the functional-differential mixed-compound equation $LQu(x,y)=0$ in the class of twice continuously differentiable solutions. Here $L$ is a differential-difference operator of mixed parabolic-elliptic type with Riemann–Liouville fractional derivative and linear shift by $y$. The $Q$ operator includes multiple functional delays and advances $a_1(x)$ and $a_2(x)$ by $x$. The functional shifts $a_1(x)$ and $a_2(x)$ are the orientation preserving mutually inverse diffeomorphisms. The integration domain is $D=D^+\cup D^-\cup I$. The “parabolicity” domain $D^+$ is the set of $(x,y)$ such that $x_0https://journals.eco-vector.com/1991-8615/article/viewFile/34678/23027mixed-compound equationfractional derivativedifference operatortricomi problem |
| spellingShingle | Alexandr Nikolaevich Zarubin Elena Viktorovna Chaplygina Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki mixed-compound equation fractional derivative difference operator tricomi problem |
| title | Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance |
| title_full | Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance |
| title_fullStr | Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance |
| title_full_unstemmed | Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance |
| title_short | Boundary value problem for mixed-compound equation with fractional derivative, functional delay and advance |
| title_sort | boundary value problem for mixed compound equation with fractional derivative functional delay and advance |
| topic | mixed-compound equation fractional derivative difference operator tricomi problem |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/34678/23027 |
| work_keys_str_mv | AT alexandrnikolaevichzarubin boundaryvalueproblemformixedcompoundequationwithfractionalderivativefunctionaldelayandadvance AT elenaviktorovnachaplygina boundaryvalueproblemformixedcompoundequationwithfractionalderivativefunctionaldelayandadvance |