A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations
Abstract This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs). Then mainly we address the error norms L2 $L_{2}$ and L∞ $L_{\infty }$ for a con...
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SpringerOpen
2020-01-01
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| Series: | Advances in Difference Equations |
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| Online Access: | https://doi.org/10.1186/s13662-019-2488-3 |
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doaj-b95909caa45940218623201abda75b292021-01-17T12:52:07ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020111810.1186/s13662-019-2488-3A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equationsSunil Kumar0Amit Kumar1Syed Abbas2Maysaa Al Qurashi3Dumitru Baleanu4Department of Mathematics, National Institute of TechnologyDepartment of Mathematics, Balarampur College PuruliaSchool of Basic Sciences, Indian Institute of Technology MandiDepartment of Mathematics, King Saud UniersityDepartment of Mathematics, Cankya UniversityAbstract This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs). Then mainly we address the error norms L2 $L_{2}$ and L∞ $L_{\infty }$ for a convergence study of the proposed method. We also find existence, uniqueness and convergence in the analysis for TFCRDEs. The projected method is illustrated by solving some numerical examples. The obtained numerical solutions by the HATM method show that it is simple to employ. An excellent conformity obtained between the solution got by the HATM method and the various well-known results available in the current literature. Also the existence and uniqueness of the solution have been demonstrated.https://doi.org/10.1186/s13662-019-2488-3Homotopy analysis transform methodFractional Cauchy reaction–diffusion equationMittag-Leffler functionOptimal value |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sunil Kumar Amit Kumar Syed Abbas Maysaa Al Qurashi Dumitru Baleanu |
| spellingShingle |
Sunil Kumar Amit Kumar Syed Abbas Maysaa Al Qurashi Dumitru Baleanu A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations Advances in Difference Equations Homotopy analysis transform method Fractional Cauchy reaction–diffusion equation Mittag-Leffler function Optimal value |
| author_facet |
Sunil Kumar Amit Kumar Syed Abbas Maysaa Al Qurashi Dumitru Baleanu |
| author_sort |
Sunil Kumar |
| title |
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations |
| title_short |
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations |
| title_full |
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations |
| title_fullStr |
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations |
| title_full_unstemmed |
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations |
| title_sort |
modified analytical approach with existence and uniqueness for fractional cauchy reaction–diffusion equations |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-01-01 |
| description |
Abstract This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction–diffusion equations (TFCRDEs). Then mainly we address the error norms L2 $L_{2}$ and L∞ $L_{\infty }$ for a convergence study of the proposed method. We also find existence, uniqueness and convergence in the analysis for TFCRDEs. The projected method is illustrated by solving some numerical examples. The obtained numerical solutions by the HATM method show that it is simple to employ. An excellent conformity obtained between the solution got by the HATM method and the various well-known results available in the current literature. Also the existence and uniqueness of the solution have been demonstrated. |
| topic |
Homotopy analysis transform method Fractional Cauchy reaction–diffusion equation Mittag-Leffler function Optimal value |
| url |
https://doi.org/10.1186/s13662-019-2488-3 |
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