Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems
In this paper, we are interested on the Shehu transform of both Prabhakar and Hilfer-Prabhakar fractional derivative and its regularized version. These results are presented in terms of Mittag-Leffler type function and also utilized to obtain the solutions of some Cauchy type problems, such as Spa...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
ATNAA
2021-03-01
|
| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1405797 |
| _version_ | 1797909710454652928 |
|---|---|
| author | Belgacem Rachid Bokhari Ahmed Sadaoui Boualem |
| author_facet | Belgacem Rachid Bokhari Ahmed Sadaoui Boualem |
| author_sort | Belgacem Rachid |
| collection | DOAJ |
| description | In this paper, we are interested on the Shehu transform of both Prabhakar and Hilfer-Prabhakar fractional
derivative and its regularized version. These results are presented in terms of Mittag-Leffler type function
and also utilized to obtain the solutions of some Cauchy type problems, such as Space-time Fractional
Advection-Dispersion equation and Generalized fractional Free Electron Laser (FEL) equation, at which
Hilfer-Prabhakar fractional derivative of fractional order and its regularized version are involved. |
| first_indexed | 2024-04-10T11:12:48Z |
| format | Article |
| id | doaj.art-b81577eba76b445a842ab81b55e3d911 |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T11:12:48Z |
| publishDate | 2021-03-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-b81577eba76b445a842ab81b55e3d9112023-02-15T16:19:01ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482021-03-015220321410.31197/atnaa.828468Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type ProblemsBelgacem RachidBokhari AhmedSadaoui BoualemIn this paper, we are interested on the Shehu transform of both Prabhakar and Hilfer-Prabhakar fractional derivative and its regularized version. These results are presented in terms of Mittag-Leffler type function and also utilized to obtain the solutions of some Cauchy type problems, such as Space-time Fractional Advection-Dispersion equation and Generalized fractional Free Electron Laser (FEL) equation, at which Hilfer-Prabhakar fractional derivative of fractional order and its regularized version are involved.https://dergipark.org.tr/tr/download/article-file/1405797prabhakar integralsshehu transformhilfer-prabhakar derivativesmittag-leffler functions |
| spellingShingle | Belgacem Rachid Bokhari Ahmed Sadaoui Boualem Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems Advances in the Theory of Nonlinear Analysis and its Applications prabhakar integrals shehu transform hilfer-prabhakar derivatives mittag-leffler functions |
| title | Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems |
| title_full | Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems |
| title_fullStr | Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems |
| title_full_unstemmed | Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems |
| title_short | Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems |
| title_sort | shehu transform of hilfer prabhakar fractional derivatives and applications on some cauchy type problems |
| topic | prabhakar integrals shehu transform hilfer-prabhakar derivatives mittag-leffler functions |
| url | https://dergipark.org.tr/tr/download/article-file/1405797 |
| work_keys_str_mv | AT belgacemrachid shehutransformofhilferprabhakarfractionalderivativesandapplicationsonsomecauchytypeproblems AT bokhariahmed shehutransformofhilferprabhakarfractionalderivativesandapplicationsonsomecauchytypeproblems AT sadaouiboualem shehutransformofhilferprabhakarfractionalderivativesandapplicationsonsomecauchytypeproblems |