Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space
Abstract A new sequence space related to the space ℓ p $\ell _{p}$ , 1 ≤ p < ∞ $1\leq p<\infty $ (the space of all absolutely p-summable sequences) is established in the present paper. It turns out that it is Banach and a BK space with Schauder basis. The Hausdorff measure of noncompactness of...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-02-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03302-2 |
| _version_ | 1818615491289153536 |
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| author | Ahmed Salem Hashim M. Alshehri Lamya Almaghamsi |
| author_facet | Ahmed Salem Hashim M. Alshehri Lamya Almaghamsi |
| author_sort | Ahmed Salem |
| collection | DOAJ |
| description | Abstract A new sequence space related to the space ℓ p $\ell _{p}$ , 1 ≤ p < ∞ $1\leq p<\infty $ (the space of all absolutely p-summable sequences) is established in the present paper. It turns out that it is Banach and a BK space with Schauder basis. The Hausdorff measure of noncompactness of this space is presented and proven. This formula with the aid the Darbo’s fixed point theorem is used to investigate the existence results for an infinite system of Langevin equations involving generalized derivative of two distinct fractional orders with three-point boundary condition. |
| first_indexed | 2024-12-16T16:34:45Z |
| format | Article |
| id | doaj.art-a703d7e98fbe4abe999a861052bc93c9 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T16:34:45Z |
| publishDate | 2021-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-a703d7e98fbe4abe999a861052bc93c92022-12-21T22:24:30ZengSpringerOpenAdvances in Difference Equations1687-18472021-02-012021112110.1186/s13662-021-03302-2Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence spaceAhmed Salem0Hashim M. Alshehri1Lamya Almaghamsi2Department of Mathematics, Faculty of Science, King Abdulaziz UniversityDepartment of Mathematics, Faculty of Science, King Abdulaziz UniversityDepartment of Mathematics, University of JeddahAbstract A new sequence space related to the space ℓ p $\ell _{p}$ , 1 ≤ p < ∞ $1\leq p<\infty $ (the space of all absolutely p-summable sequences) is established in the present paper. It turns out that it is Banach and a BK space with Schauder basis. The Hausdorff measure of noncompactness of this space is presented and proven. This formula with the aid the Darbo’s fixed point theorem is used to investigate the existence results for an infinite system of Langevin equations involving generalized derivative of two distinct fractional orders with three-point boundary condition.https://doi.org/10.1186/s13662-021-03302-2Infinite systemFraction Langevin equationMeasure of noncompactnessDarbo’s fixed point theoremSequence space |
| spellingShingle | Ahmed Salem Hashim M. Alshehri Lamya Almaghamsi Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space Advances in Difference Equations Infinite system Fraction Langevin equation Measure of noncompactness Darbo’s fixed point theorem Sequence space |
| title | Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space |
| title_full | Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space |
| title_fullStr | Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space |
| title_full_unstemmed | Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space |
| title_short | Measure of noncompactness for an infinite system of fractional Langevin equation in a sequence space |
| title_sort | measure of noncompactness for an infinite system of fractional langevin equation in a sequence space |
| topic | Infinite system Fraction Langevin equation Measure of noncompactness Darbo’s fixed point theorem Sequence space |
| url | https://doi.org/10.1186/s13662-021-03302-2 |
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