Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation
The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2016-09-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/18/9/329 |
| _version_ | 1798042937855049728 |
|---|---|
| author | Neeraj Kumar Tripathi Subir Das Seng Huat Ong Hossein Jafari Maysaa Al Qurashi |
| author_facet | Neeraj Kumar Tripathi Subir Das Seng Huat Ong Hossein Jafari Maysaa Al Qurashi |
| author_sort | Neeraj Kumar Tripathi |
| collection | DOAJ |
| description | The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various anomalous exponents of particular cases, to predict damping of the field variable. Numerical computations of the convergence control parameter, used to evaluate the convergence of approximate series solution through minimizing error, are also presented graphically for these cases. |
| first_indexed | 2024-04-11T22:42:27Z |
| format | Article |
| id | doaj.art-66808a9edf9f44b1b874ae5f7e36faa0 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:42:27Z |
| publishDate | 2016-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-66808a9edf9f44b1b874ae5f7e36faa02022-12-22T03:58:57ZengMDPI AGEntropy1099-43002016-09-0118932910.3390/e18090329e18090329Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion EquationNeeraj Kumar Tripathi0Subir Das1Seng Huat Ong2Hossein Jafari3Maysaa Al Qurashi4Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221 005, IndiaDepartment of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221 005, IndiaInstitute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, MalaysiaDepartment of Mathematical Sciences, University of South Africa, UNISA, Pretoria 0003, South AfricaDepartment of Mathematics, King Saud University, Riyadh 11495, Saudi ArabiaThe approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various anomalous exponents of particular cases, to predict damping of the field variable. Numerical computations of the convergence control parameter, used to evaluate the convergence of approximate series solution through minimizing error, are also presented graphically for these cases.http://www.mdpi.com/1099-4300/18/9/329fractional order systemdiffusion-reaction equationhomotopy analysis methodconvergence analysis |
| spellingShingle | Neeraj Kumar Tripathi Subir Das Seng Huat Ong Hossein Jafari Maysaa Al Qurashi Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation Entropy fractional order system diffusion-reaction equation homotopy analysis method convergence analysis |
| title | Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation |
| title_full | Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation |
| title_fullStr | Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation |
| title_full_unstemmed | Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation |
| title_short | Solution of Higher Order Nonlinear Time-Fractional Reaction Diffusion Equation |
| title_sort | solution of higher order nonlinear time fractional reaction diffusion equation |
| topic | fractional order system diffusion-reaction equation homotopy analysis method convergence analysis |
| url | http://www.mdpi.com/1099-4300/18/9/329 |
| work_keys_str_mv | AT neerajkumartripathi solutionofhigherordernonlineartimefractionalreactiondiffusionequation AT subirdas solutionofhigherordernonlineartimefractionalreactiondiffusionequation AT senghuatong solutionofhigherordernonlineartimefractionalreactiondiffusionequation AT hosseinjafari solutionofhigherordernonlineartimefractionalreactiondiffusionequation AT maysaaalqurashi solutionofhigherordernonlineartimefractionalreactiondiffusionequation |