Analytical solution of a fractional differential equation in the theory of viscoelastic fluids
The aim of this paper is to present analytical solutions of fractional delay differential equations (FDDEs) of an incompressible generalized Oldroyd-B fluid with fractional derivatives of Caputo type. Using a modification of the method of separation of variables the main equation with non-h...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2021-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2021-103-3/11.pdf |
| _version_ | 1797686739808026624 |
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| author | S. Saghali F.D. Saei M. Javidi M.J. Rad |
| author_facet | S. Saghali F.D. Saei M. Javidi M.J. Rad |
| author_sort | S. Saghali |
| collection | DOAJ |
| description | The aim of this paper is to present analytical solutions of fractional delay differential equations (FDDEs) of an incompressible generalized Oldroyd-B fluid with fractional derivatives of Caputo type. Using a modification of the method of separation of variables the main equation with non-homogeneous boundary conditions is transformed into an equation with homogeneous boundary conditions, and the resulting solutions are then expressed in terms of Green functions via Laplace transforms. This results presented in two condition, in first step when 0 ≤ α, β ≤ 1/2 and in the second step we considered 1/2 ≤ α, β ≤ 1, for each step 1,2 for the unsteady flows of a generalized Oldroyd-B fluid, including a flow with a moving plate, are considered via examples. |
| first_indexed | 2024-03-12T01:10:14Z |
| format | Article |
| id | doaj.art-dbdb1f976add4ffbaeb95fc80ea13a92 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:10:14Z |
| publishDate | 2021-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-dbdb1f976add4ffbaeb95fc80ea13a922023-09-14T06:33:42ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112021-09-01103310511610.31489/2021M3/105-116Analytical solution of a fractional differential equation in the theory of viscoelastic fluidsS. SaghaliF.D. SaeiM. JavidiM.J. Rad The aim of this paper is to present analytical solutions of fractional delay differential equations (FDDEs) of an incompressible generalized Oldroyd-B fluid with fractional derivatives of Caputo type. Using a modification of the method of separation of variables the main equation with non-homogeneous boundary conditions is transformed into an equation with homogeneous boundary conditions, and the resulting solutions are then expressed in terms of Green functions via Laplace transforms. This results presented in two condition, in first step when 0 ≤ α, β ≤ 1/2 and in the second step we considered 1/2 ≤ α, β ≤ 1, for each step 1,2 for the unsteady flows of a generalized Oldroyd-B fluid, including a flow with a moving plate, are considered via examples.https://mathematics-vestnik.ksu.kz/apart/2021-103-3/11.pdf |
| spellingShingle | S. Saghali F.D. Saei M. Javidi M.J. Rad Analytical solution of a fractional differential equation in the theory of viscoelastic fluids Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Analytical solution of a fractional differential equation in the theory of viscoelastic fluids |
| title_full | Analytical solution of a fractional differential equation in the theory of viscoelastic fluids |
| title_fullStr | Analytical solution of a fractional differential equation in the theory of viscoelastic fluids |
| title_full_unstemmed | Analytical solution of a fractional differential equation in the theory of viscoelastic fluids |
| title_short | Analytical solution of a fractional differential equation in the theory of viscoelastic fluids |
| title_sort | analytical solution of a fractional differential equation in the theory of viscoelastic fluids |
| url | https://mathematics-vestnik.ksu.kz/apart/2021-103-3/11.pdf |
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