Fractional q-symmetric calculus on a time scale
Abstract In this paper, the definitions of q-symmetric exponential function and q-symmetric gamma function are presented. By a q-symmetric exponential function, we shall illustrate the Laplace transform method and define and solve several families of linear fractional q-symmetric difference equation...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1219-x |
| _version_ | 1811338569240805376 |
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| author | Mingzhe Sun Chengmin Hou |
| author_facet | Mingzhe Sun Chengmin Hou |
| author_sort | Mingzhe Sun |
| collection | DOAJ |
| description | Abstract In this paper, the definitions of q-symmetric exponential function and q-symmetric gamma function are presented. By a q-symmetric exponential function, we shall illustrate the Laplace transform method and define and solve several families of linear fractional q-symmetric difference equations with constant coefficients. We also introduce a q-symmetric analogue Mittag-Leffler function and study q-symmetric Caputo fractional initial value problems. It is hoped that our work will provide foundation and motivation for further studying of fractional q-symmetric difference systems. |
| first_indexed | 2024-04-13T18:12:46Z |
| format | Article |
| id | doaj.art-17ab77d2fa5d4e6e92720082369dce42 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-13T18:12:46Z |
| publishDate | 2017-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-17ab77d2fa5d4e6e92720082369dce422022-12-22T02:35:48ZengSpringerOpenAdvances in Difference Equations1687-18472017-06-012017111810.1186/s13662-017-1219-xFractional q-symmetric calculus on a time scaleMingzhe Sun0Chengmin Hou1Department of Mathematics, Yanbian UniversityDepartment of Mathematics, Yanbian UniversityAbstract In this paper, the definitions of q-symmetric exponential function and q-symmetric gamma function are presented. By a q-symmetric exponential function, we shall illustrate the Laplace transform method and define and solve several families of linear fractional q-symmetric difference equations with constant coefficients. We also introduce a q-symmetric analogue Mittag-Leffler function and study q-symmetric Caputo fractional initial value problems. It is hoped that our work will provide foundation and motivation for further studying of fractional q-symmetric difference systems.http://link.springer.com/article/10.1186/s13662-017-1219-xfractional q-symmetric exponential functionfractional q-symmetric gamma functionLaplace transforminitial value problem |
| spellingShingle | Mingzhe Sun Chengmin Hou Fractional q-symmetric calculus on a time scale Advances in Difference Equations fractional q-symmetric exponential function fractional q-symmetric gamma function Laplace transform initial value problem |
| title | Fractional q-symmetric calculus on a time scale |
| title_full | Fractional q-symmetric calculus on a time scale |
| title_fullStr | Fractional q-symmetric calculus on a time scale |
| title_full_unstemmed | Fractional q-symmetric calculus on a time scale |
| title_short | Fractional q-symmetric calculus on a time scale |
| title_sort | fractional q symmetric calculus on a time scale |
| topic | fractional q-symmetric exponential function fractional q-symmetric gamma function Laplace transform initial value problem |
| url | http://link.springer.com/article/10.1186/s13662-017-1219-x |
| work_keys_str_mv | AT mingzhesun fractionalqsymmetriccalculusonatimescale AT chengminhou fractionalqsymmetriccalculusonatimescale |