Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable
Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/4797955 |
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| author | Najla M. Alarifi Rabha W. Ibrahim |
| author_facet | Najla M. Alarifi Rabha W. Ibrahim |
| author_sort | Najla M. Alarifi |
| collection | DOAJ |
| description | Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope. |
| format | Article |
| id | doaj-art-b96604abf18642ed9ed0b2ac722b3cbe |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-b96604abf18642ed9ed0b2ac722b3cbe2025-02-03T01:25:09ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/47979554797955Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex VariableNajla M. Alarifi0Rabha W. Ibrahim1Department of Mathematics, Imam Abdulrahman Bin Faisal University, Dammam 31113, Saudi ArabiaIEEE: 94086547, Kuala Lumpur 59200, MalaysiaSaint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope.http://dx.doi.org/10.1155/2021/4797955 |
| spellingShingle | Najla M. Alarifi Rabha W. Ibrahim Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable Journal of Function Spaces |
| title | Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable |
| title_full | Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable |
| title_fullStr | Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable |
| title_full_unstemmed | Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable |
| title_short | Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable |
| title_sort | analytic normalized solutions of 2d fractional saint venant equations of a complex variable |
| url | http://dx.doi.org/10.1155/2021/4797955 |
| work_keys_str_mv | AT najlamalarifi analyticnormalizedsolutionsof2dfractionalsaintvenantequationsofacomplexvariable AT rabhawibrahim analyticnormalizedsolutionsof2dfractionalsaintvenantequationsofacomplexvariable |