Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives
In this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011)] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1]. We prove some interesting properties of the fractional integrals and derivat...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2017-03-01
|
| Series: | International Journal of Analysis and Applications |
| Online Access: | http://www.etamaths.com/index.php/ijaa/article/view/1013 |
| _version_ | 1818681208227233792 |
|---|---|
| author | Basak Karpuz Umut M. Ozkan Tugba Yalcin Mustafa K. Yildiz |
| author_facet | Basak Karpuz Umut M. Ozkan Tugba Yalcin Mustafa K. Yildiz |
| author_sort | Basak Karpuz |
| collection | DOAJ |
| description | In this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011)] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1]. We prove some interesting properties of the fractional integrals and derivatives. Based on these properties, the following concepts for the new type fractional differential equations are explored: Existence and uniqueness of solutions; Solutions of autonomous fractional differential equations; Dependence on the initial conditions; Green’s function; Variation of parameters formula. |
| first_indexed | 2024-12-17T09:59:17Z |
| format | Article |
| id | doaj.art-c0679e833251495d90345b1e3da8908d |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-17T09:59:17Z |
| publishDate | 2017-03-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-c0679e833251495d90345b1e3da8908d2022-12-21T21:53:21ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392017-03-01132216230231Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional DerivativesBasak Karpuz0Umut M. Ozkan1Tugba Yalcin2Mustafa K. Yildiz3Dokuz Eylul UniversityAfyon Kocatepe UniversityAfyon Kocatepe UniversityAfyon Kocatepe UniversityIn this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011)] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1]. We prove some interesting properties of the fractional integrals and derivatives. Based on these properties, the following concepts for the new type fractional differential equations are explored: Existence and uniqueness of solutions; Solutions of autonomous fractional differential equations; Dependence on the initial conditions; Green’s function; Variation of parameters formula.http://www.etamaths.com/index.php/ijaa/article/view/1013 |
| spellingShingle | Basak Karpuz Umut M. Ozkan Tugba Yalcin Mustafa K. Yildiz Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives International Journal of Analysis and Applications |
| title | Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives |
| title_full | Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives |
| title_fullStr | Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives |
| title_full_unstemmed | Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives |
| title_short | Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives |
| title_sort | basic theory for differential equations with unified reimann liouville and hadamard type fractional derivatives |
| url | http://www.etamaths.com/index.php/ijaa/article/view/1013 |
| work_keys_str_mv | AT basakkarpuz basictheoryfordifferentialequationswithunifiedreimannliouvilleandhadamardtypefractionalderivatives AT umutmozkan basictheoryfordifferentialequationswithunifiedreimannliouvilleandhadamardtypefractionalderivatives AT tugbayalcin basictheoryfordifferentialequationswithunifiedreimannliouvilleandhadamardtypefractionalderivatives AT mustafakyildiz basictheoryfordifferentialequationswithunifiedreimannliouvilleandhadamardtypefractionalderivatives |