Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series
In this work, we define a new class of functions of the Bernoulli type using the Riemann-Liouville fractional integral operator and derive a generating function for these class generalized functions. Then, these functions are employed to derive formulas for certain Dirichlet series.
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/4875916 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549492474249216 |
|---|---|
| author | Jorge Sanchez-Ortiz |
| author_facet | Jorge Sanchez-Ortiz |
| author_sort | Jorge Sanchez-Ortiz |
| collection | DOAJ |
| description | In this work, we define a new class of functions of the Bernoulli type using the Riemann-Liouville fractional integral operator and derive a generating function for these class generalized functions. Then, these functions are employed to derive formulas for certain Dirichlet series. |
| format | Article |
| id | doaj-art-1f1ad0a2aee24cb48053f63aa4c46606 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1f1ad0a2aee24cb48053f63aa4c466062025-02-03T06:11:11ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/48759164875916Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet SeriesJorge Sanchez-Ortiz0Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, México, CP 39087, MexicoIn this work, we define a new class of functions of the Bernoulli type using the Riemann-Liouville fractional integral operator and derive a generating function for these class generalized functions. Then, these functions are employed to derive formulas for certain Dirichlet series.http://dx.doi.org/10.1155/2018/4875916 |
| spellingShingle | Jorge Sanchez-Ortiz Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series Abstract and Applied Analysis |
| title | Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series |
| title_full | Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series |
| title_fullStr | Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series |
| title_full_unstemmed | Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series |
| title_short | Generalized Fractional-Order Bernoulli Functions via Riemann-Liouville Operator and Their Applications in the Evaluation of Dirichlet Series |
| title_sort | generalized fractional order bernoulli functions via riemann liouville operator and their applications in the evaluation of dirichlet series |
| url | http://dx.doi.org/10.1155/2018/4875916 |
| work_keys_str_mv | AT jorgesanchezortiz generalizedfractionalorderbernoullifunctionsviariemannliouvilleoperatorandtheirapplicationsintheevaluationofdirichletseries |