On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform
The Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively....
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/7767848 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832557095010959360 |
|---|---|
| author | Saima Rashid Sobia Sultana Rehana Ashraf Mohammed K. A. Kaabar |
| author_facet | Saima Rashid Sobia Sultana Rehana Ashraf Mohammed K. A. Kaabar |
| author_sort | Saima Rashid |
| collection | DOAJ |
| description | The Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively. The Jafari transform is merged with the Adomian decomposition method and new iterative transform method. It is worth mentioning that the Jafari transform is the unification of several existing transforms. Besides that, the convergence and uniqueness results are carried out for the aforesaid model. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest its applicability for a variety of nonlinear evolutionary problems. |
| format | Article |
| id | doaj-art-510b6d2c98924148a54b6d679c38f59b |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-510b6d2c98924148a54b6d679c38f59b2025-02-03T05:43:34ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/7767848On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari TransformSaima Rashid0Sobia Sultana1Rehana Ashraf2Mohammed K. A. Kaabar3Department of MathematicsDepartment of MathematicsDepartment of MathematicsGofa CampThe Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively. The Jafari transform is merged with the Adomian decomposition method and new iterative transform method. It is worth mentioning that the Jafari transform is the unification of several existing transforms. Besides that, the convergence and uniqueness results are carried out for the aforesaid model. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest its applicability for a variety of nonlinear evolutionary problems.http://dx.doi.org/10.1155/2021/7767848 |
| spellingShingle | Saima Rashid Sobia Sultana Rehana Ashraf Mohammed K. A. Kaabar On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform Journal of Function Spaces |
| title | On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform |
| title_full | On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform |
| title_fullStr | On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform |
| title_full_unstemmed | On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform |
| title_short | On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform |
| title_sort | on comparative analysis for the black scholes model in the generalized fractional derivatives sense via jafari transform |
| url | http://dx.doi.org/10.1155/2021/7767848 |
| work_keys_str_mv | AT saimarashid oncomparativeanalysisfortheblackscholesmodelinthegeneralizedfractionalderivativessenseviajafaritransform AT sobiasultana oncomparativeanalysisfortheblackscholesmodelinthegeneralizedfractionalderivativessenseviajafaritransform AT rehanaashraf oncomparativeanalysisfortheblackscholesmodelinthegeneralizedfractionalderivativessenseviajafaritransform AT mohammedkakaabar oncomparativeanalysisfortheblackscholesmodelinthegeneralizedfractionalderivativessenseviajafaritransform |