Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation
We use the fractional derivatives in modified Riemann-Liouville derivative sense to construct exact solutions of time fractional simplified modified Camassa-Holm (MCH) equation. A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/601961 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849409605160927232 |
|---|---|
| author | Muhammad Shakeel Qazi Mahmood Ul-Hassan Jamshad Ahmad |
| author_facet | Muhammad Shakeel Qazi Mahmood Ul-Hassan Jamshad Ahmad |
| author_sort | Muhammad Shakeel |
| collection | DOAJ |
| description | We use the fractional derivatives in modified Riemann-Liouville derivative sense to construct exact solutions of time fractional simplified modified Camassa-Holm (MCH) equation. A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and, as a result, many exact analytical solutions are obtained with more free parameters. When these free parameters are taken as particular values, the traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. Moreover, the numerical presentations of some of the solutions have been demonstrated with the aid of commercial software Maple. The recital of the method is trustworthy and useful and gives more new general exact solutions. |
| format | Article |
| id | doaj-art-7cadcf88fd8840d0b8a23f0efcc039c1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7cadcf88fd8840d0b8a23f0efcc039c12025-08-20T03:35:27ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/601961601961Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) EquationMuhammad Shakeel0Qazi Mahmood Ul-Hassan1Jamshad Ahmad2Department of Mathematics, Faculty of Sciences, HITEC University, Taxila 47080, PakistanDepartment of Mathematics, Faculty of Sciences, HITEC University, Taxila 47080, PakistanDepartment of Mathematics, Faculty of Sciences, HITEC University, Taxila 47080, PakistanWe use the fractional derivatives in modified Riemann-Liouville derivative sense to construct exact solutions of time fractional simplified modified Camassa-Holm (MCH) equation. A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and, as a result, many exact analytical solutions are obtained with more free parameters. When these free parameters are taken as particular values, the traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. Moreover, the numerical presentations of some of the solutions have been demonstrated with the aid of commercial software Maple. The recital of the method is trustworthy and useful and gives more new general exact solutions.http://dx.doi.org/10.1155/2014/601961 |
| spellingShingle | Muhammad Shakeel Qazi Mahmood Ul-Hassan Jamshad Ahmad Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation Abstract and Applied Analysis |
| title | Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation |
| title_full | Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation |
| title_fullStr | Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation |
| title_full_unstemmed | Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation |
| title_short | Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation |
| title_sort | applications of the novel g g expansion method for a time fractional simplified modified camassa holm mch equation |
| url | http://dx.doi.org/10.1155/2014/601961 |
| work_keys_str_mv | AT muhammadshakeel applicationsofthenovelggexpansionmethodforatimefractionalsimplifiedmodifiedcamassaholmmchequation AT qazimahmoodulhassan applicationsofthenovelggexpansionmethodforatimefractionalsimplifiedmodifiedcamassaholmmchequation AT jamshadahmad applicationsofthenovelggexpansionmethodforatimefractionalsimplifiedmodifiedcamassaholmmchequation |