Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces
Abstract This paper deals with the existence results of the infinite system of tempered fractional BVPs D r ϱ , λ 0 R z j ( r ) + ψ j ( r , z ( r ) ) = 0 , 0 < r < 1 , z j ( 0 ) = 0 , 0 R D r m , λ z j ( 0 ) = 0 , b 1 z j ( 1 ) + b 2 0 R D r m , λ z j ( 1 ) = 0 , $$\begin{aligned}& {}^{\ma...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-02-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01826-6 |
| _version_ | 1797273818930085888 |
|---|---|
| author | Sabbavarapu Nageswara Rao Mahammad Khuddush Ahmed Hussein Msmali Abdullah Ali H. Ahmadini |
| author_facet | Sabbavarapu Nageswara Rao Mahammad Khuddush Ahmed Hussein Msmali Abdullah Ali H. Ahmadini |
| author_sort | Sabbavarapu Nageswara Rao |
| collection | DOAJ |
| description | Abstract This paper deals with the existence results of the infinite system of tempered fractional BVPs D r ϱ , λ 0 R z j ( r ) + ψ j ( r , z ( r ) ) = 0 , 0 < r < 1 , z j ( 0 ) = 0 , 0 R D r m , λ z j ( 0 ) = 0 , b 1 z j ( 1 ) + b 2 0 R D r m , λ z j ( 1 ) = 0 , $$\begin{aligned}& {}^{\mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\varrho , \uplambda} \mathtt{z}_{\mathtt{j}}(\mathrm{r})+\psi _{\mathtt{j}}\bigl(\mathrm{r}, \mathtt{z}(\mathrm{r})\bigr)=0,\quad 0< \mathrm{r}< 1, \\& \mathtt{z}_{\mathtt{j}}(0)=0,\qquad {}^{\mathtt{R}}_{0} \mathrm{D}_{ \mathrm{r}}^{\mathtt{m}, \uplambda} \mathtt{z}_{\mathtt{j}}(0)=0, \\& \mathtt{b}_{1} \mathtt{z}_{\mathtt{j}}(1)+\mathtt{b}_{2} {}^{ \mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\mathtt{m}, \uplambda} \mathtt{z}_{\mathtt{j}}(1)=0, \end{aligned}$$ where j ∈ N $\mathtt{j}\in \mathbb{N}$ , 2 < ϱ ≤ 3 $2<\varrho \le 3$ , 1 < m ≤ 2 $1<\mathtt{m}\le 2$ , by utilizing the Hausdorff measure of noncompactness and Meir–Keeler fixed point theorem in a tempered sequence space. |
| first_indexed | 2024-03-07T14:49:40Z |
| format | Article |
| id | doaj.art-769c1aaeb25b452681cde1afba1fcb11 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-07T14:49:40Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-769c1aaeb25b452681cde1afba1fcb112024-03-05T19:48:02ZengSpringerOpenBoundary Value Problems1687-27702024-02-012024111710.1186/s13661-024-01826-6Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spacesSabbavarapu Nageswara Rao0Mahammad Khuddush1Ahmed Hussein Msmali2Abdullah Ali H. Ahmadini3Department of Mathematics, College of Science, Jazan UniversityDepartment of Mathematics, Chegg India Pvt. Ltd.Department of Mathematics, College of Science, Jazan UniversityDepartment of Mathematics, College of Science, Jazan UniversityAbstract This paper deals with the existence results of the infinite system of tempered fractional BVPs D r ϱ , λ 0 R z j ( r ) + ψ j ( r , z ( r ) ) = 0 , 0 < r < 1 , z j ( 0 ) = 0 , 0 R D r m , λ z j ( 0 ) = 0 , b 1 z j ( 1 ) + b 2 0 R D r m , λ z j ( 1 ) = 0 , $$\begin{aligned}& {}^{\mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\varrho , \uplambda} \mathtt{z}_{\mathtt{j}}(\mathrm{r})+\psi _{\mathtt{j}}\bigl(\mathrm{r}, \mathtt{z}(\mathrm{r})\bigr)=0,\quad 0< \mathrm{r}< 1, \\& \mathtt{z}_{\mathtt{j}}(0)=0,\qquad {}^{\mathtt{R}}_{0} \mathrm{D}_{ \mathrm{r}}^{\mathtt{m}, \uplambda} \mathtt{z}_{\mathtt{j}}(0)=0, \\& \mathtt{b}_{1} \mathtt{z}_{\mathtt{j}}(1)+\mathtt{b}_{2} {}^{ \mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\mathtt{m}, \uplambda} \mathtt{z}_{\mathtt{j}}(1)=0, \end{aligned}$$ where j ∈ N $\mathtt{j}\in \mathbb{N}$ , 2 < ϱ ≤ 3 $2<\varrho \le 3$ , 1 < m ≤ 2 $1<\mathtt{m}\le 2$ , by utilizing the Hausdorff measure of noncompactness and Meir–Keeler fixed point theorem in a tempered sequence space.https://doi.org/10.1186/s13661-024-01826-6Tempered fractional derivativeMeasure of noncompactnessMeir–Keeler fixed point theoremTempered sequence spaces |
| spellingShingle | Sabbavarapu Nageswara Rao Mahammad Khuddush Ahmed Hussein Msmali Abdullah Ali H. Ahmadini Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces Boundary Value Problems Tempered fractional derivative Measure of noncompactness Meir–Keeler fixed point theorem Tempered sequence spaces |
| title | Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces |
| title_full | Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces |
| title_fullStr | Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces |
| title_full_unstemmed | Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces |
| title_short | Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces |
| title_sort | infinite system of nonlinear tempered fractional order bvps in tempered sequence spaces |
| topic | Tempered fractional derivative Measure of noncompactness Meir–Keeler fixed point theorem Tempered sequence spaces |
| url | https://doi.org/10.1186/s13661-024-01826-6 |
| work_keys_str_mv | AT sabbavarapunageswararao infinitesystemofnonlineartemperedfractionalorderbvpsintemperedsequencespaces AT mahammadkhuddush infinitesystemofnonlineartemperedfractionalorderbvpsintemperedsequencespaces AT ahmedhusseinmsmali infinitesystemofnonlineartemperedfractionalorderbvpsintemperedsequencespaces AT abdullahalihahmadini infinitesystemofnonlineartemperedfractionalorderbvpsintemperedsequencespaces |