Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative
In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo (ABC) is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DS...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/4475491 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565453048774656 |
|---|---|
| author | Fareeha Sami Khan M. Khalid Omar Bazighifan A. El-Mesady |
| author_facet | Fareeha Sami Khan M. Khalid Omar Bazighifan A. El-Mesady |
| author_sort | Fareeha Sami Khan |
| collection | DOAJ |
| description | In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo (ABC) is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α∈0,1 and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h. |
| format | Article |
| id | doaj-art-805be4b3dda1456cb5d936b80eea22c0 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-805be4b3dda1456cb5d936b80eea22c02025-02-03T01:07:36ZengWileyComplexity1099-05262022-01-01202210.1155/2022/4475491Euler’s Numerical Method on Fractional DSEK Model under ABC DerivativeFareeha Sami Khan0M. Khalid1Omar Bazighifan2A. El-Mesady3112Department of Physics and Engineering MathematicsIn this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo (ABC) is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α∈0,1 and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h.http://dx.doi.org/10.1155/2022/4475491 |
| spellingShingle | Fareeha Sami Khan M. Khalid Omar Bazighifan A. El-Mesady Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative Complexity |
| title | Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative |
| title_full | Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative |
| title_fullStr | Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative |
| title_full_unstemmed | Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative |
| title_short | Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative |
| title_sort | euler s numerical method on fractional dsek model under abc derivative |
| url | http://dx.doi.org/10.1155/2022/4475491 |
| work_keys_str_mv | AT fareehasamikhan eulersnumericalmethodonfractionaldsekmodelunderabcderivative AT mkhalid eulersnumericalmethodonfractionaldsekmodelunderabcderivative AT omarbazighifan eulersnumericalmethodonfractionaldsekmodelunderabcderivative AT aelmesady eulersnumericalmethodonfractionaldsekmodelunderabcderivative |