Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems
In this paper the existence of unique positive solutions for system of (p, q, r)-Lapalacian Sturm-Liouville type two-point fractional order boundary vaue problems, CDα 0+ φp(u(t)) + f t, u(t), v(t), w(t) = 0, 0 < t < 1, CD β 0+ φq(v(t)) + g t, v(t), w(t), u(t) = 0, 0...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
ATNAA
2021-02-01
|
| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1005037 |
| _version_ | 1797923980422676480 |
|---|---|
| author | K. Rajendra Prasad D. Leela Mahammad Khuddush |
| author_facet | K. Rajendra Prasad D. Leela Mahammad Khuddush |
| author_sort | K. Rajendra Prasad |
| collection | DOAJ |
| description | In this paper the existence of unique positive solutions for system of (p, q, r)-Lapalacian Sturm-Liouville type
two-point fractional order boundary vaue problems,
CDα
0+
φp(u(t))
+ f
t, u(t), v(t), w(t)
= 0, 0 < t < 1,
CD
β
0+
φq(v(t))
+ g
t, v(t), w(t), u(t)
= 0, 0 < t < 1,
CD
γ
0+
φr(w(t))
+ h
t, w(t), u(t), v(t)
= 0, 0 < t < 1,
a1(φpu)(0) − b1(φpu)
0
(0) = 0, c1(φpu)(1) + d1(φpu)
0
(1) = 0,
a2(φqv)(0) − b2(φqv)
0
(0) = 0, c2(φqv)(1) + d2(φqv)
0
(1) = 0,
a3(φrw)(0) − b3(φrw)
0
(0) = 0, c3(φrw)(1) + d3(φrw)
0
(1) = 0,
where 1 < α, β, γ ≤ 2, φ`(τ) = |τ|
`−2τ, ` ∈ (1, ∞),
CD?
0+ is a Caputo fractional derivatives of order
? ∈ {α, β, γ} and ai
, bi
, ci
, di
, i = 1, 2, 3 are positive constants, is established by an application of n-fixed
point theorem of ternary operators on partially ordered metric spaces |
| first_indexed | 2024-04-10T14:55:34Z |
| format | Article |
| id | doaj.art-829a5f41a41a4f158494b6150695da9d |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T14:55:34Z |
| publishDate | 2021-02-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-829a5f41a41a4f158494b6150695da9d2023-02-15T16:07:24ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482021-02-015113815710.31197/atnaa.703304Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problemsK. Rajendra PrasadD. LeelaMahammad KhuddushIn this paper the existence of unique positive solutions for system of (p, q, r)-Lapalacian Sturm-Liouville type two-point fractional order boundary vaue problems, CDα 0+ φp(u(t)) + f t, u(t), v(t), w(t) = 0, 0 < t < 1, CD β 0+ φq(v(t)) + g t, v(t), w(t), u(t) = 0, 0 < t < 1, CD γ 0+ φr(w(t)) + h t, w(t), u(t), v(t) = 0, 0 < t < 1, a1(φpu)(0) − b1(φpu) 0 (0) = 0, c1(φpu)(1) + d1(φpu) 0 (1) = 0, a2(φqv)(0) − b2(φqv) 0 (0) = 0, c2(φqv)(1) + d2(φqv) 0 (1) = 0, a3(φrw)(0) − b3(φrw) 0 (0) = 0, c3(φrw)(1) + d3(φrw) 0 (1) = 0, where 1 < α, β, γ ≤ 2, φ`(τ) = |τ| `−2τ, ` ∈ (1, ∞), CD? 0+ is a Caputo fractional derivatives of order ? ∈ {α, β, γ} and ai , bi , ci , di , i = 1, 2, 3 are positive constants, is established by an application of n-fixed point theorem of ternary operators on partially ordered metric spaceshttps://dergipark.org.tr/tr/download/article-file/1005037caputo fractional derivativepositive solutionmonotone mappingspartially ordered complete metric spacescontractiveboundary value problemn-fixed point |
| spellingShingle | K. Rajendra Prasad D. Leela Mahammad Khuddush Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems Advances in the Theory of Nonlinear Analysis and its Applications caputo fractional derivative positive solution monotone mappings partially ordered complete metric spaces contractive boundary value problem n-fixed point |
| title | Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems |
| title_full | Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems |
| title_fullStr | Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems |
| title_full_unstemmed | Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems |
| title_short | Existence and uniqueness of positive solutions for system of (p, q, r)-Laplacian fractional order boundary value problems |
| title_sort | existence and uniqueness of positive solutions for system of p q r laplacian fractional order boundary value problems |
| topic | caputo fractional derivative positive solution monotone mappings partially ordered complete metric spaces contractive boundary value problem n-fixed point |
| url | https://dergipark.org.tr/tr/download/article-file/1005037 |
| work_keys_str_mv | AT krajendraprasad existenceanduniquenessofpositivesolutionsforsystemofpqrlaplacianfractionalorderboundaryvalueproblems AT dleela existenceanduniquenessofpositivesolutionsforsystemofpqrlaplacianfractionalorderboundaryvalueproblems AT mahammadkhuddush existenceanduniquenessofpositivesolutionsforsystemofpqrlaplacianfractionalorderboundaryvalueproblems |