Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity
Abstract This work uses the modified Extended Direct Algebraic Method (mEDAM) with conformable derivatives to obtain accurate solutions for the diffusion-reaction equation with cubic nonlinearity and the nonlinear fractional generalised density-independent DR problem. We use fractional derivatives i...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-01997-w |
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| _version_ | 1823861730952871936 |
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| author | Muhammad Bilal Alamgir Khan Ikram Ullah Hasib Khan Jehad Alzabut Hisham Mohammad Alkhawar |
| author_facet | Muhammad Bilal Alamgir Khan Ikram Ullah Hasib Khan Jehad Alzabut Hisham Mohammad Alkhawar |
| author_sort | Muhammad Bilal |
| collection | DOAJ |
| description | Abstract This work uses the modified Extended Direct Algebraic Method (mEDAM) with conformable derivatives to obtain accurate solutions for the diffusion-reaction equation with cubic nonlinearity and the nonlinear fractional generalised density-independent DR problem. We use fractional derivatives in the conformable sense to achieve precise polynomial-form solutions by converting the equations into autonomous two-dimensional plane systems. The technique solves nonlinear ordinary differential equations (ODEs) produced by a fractional transformation to produce travelling wave solutions. Through the visualisation of various solution profiles, as periodic, shock, kink, anti-kink, and soliton waves, numerical simulations offer important insights into the dynamics of nonlinear fractional partial differential equations. This work builds on earlier research and broadens our understanding of complex events. |
| format | Article |
| id | doaj-art-76c9c6c206124452aeed14105527fa3b |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-76c9c6c206124452aeed14105527fa3b2025-02-09T12:47:43ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025112710.1186/s13661-025-01997-wApplication of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearityMuhammad Bilal0Alamgir Khan1Ikram Ullah2Hasib Khan3Jehad Alzabut4Hisham Mohammad Alkhawar5Department of Mathematics, Abdul Wali Khan UniversitySchool of Mathematics and Statistics, Central South UniversitySchool of Mathematics and Statistics, Central South UniversityDepartment of Mathematics and Sciences, Prince Sultan UniversityDepartment of Mathematics and Sciences, Prince Sultan UniversityPreparatory Year Program, Computer Department, Prince Sultan UniversityAbstract This work uses the modified Extended Direct Algebraic Method (mEDAM) with conformable derivatives to obtain accurate solutions for the diffusion-reaction equation with cubic nonlinearity and the nonlinear fractional generalised density-independent DR problem. We use fractional derivatives in the conformable sense to achieve precise polynomial-form solutions by converting the equations into autonomous two-dimensional plane systems. The technique solves nonlinear ordinary differential equations (ODEs) produced by a fractional transformation to produce travelling wave solutions. Through the visualisation of various solution profiles, as periodic, shock, kink, anti-kink, and soliton waves, numerical simulations offer important insights into the dynamics of nonlinear fractional partial differential equations. This work builds on earlier research and broadens our understanding of complex events.https://doi.org/10.1186/s13661-025-01997-wmEDAM techniqueConformable derivativesSolitonsPartial differential equationsDensity-independent DR equationCubic nonlinearity |
| spellingShingle | Muhammad Bilal Alamgir Khan Ikram Ullah Hasib Khan Jehad Alzabut Hisham Mohammad Alkhawar Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity Boundary Value Problems mEDAM technique Conformable derivatives Solitons Partial differential equations Density-independent DR equation Cubic nonlinearity |
| title | Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity |
| title_full | Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity |
| title_fullStr | Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity |
| title_full_unstemmed | Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity |
| title_short | Application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity |
| title_sort | application of modified extended direct algebraic method to nonlinear fractional diffusion reaction equation with cubic nonlinearity |
| topic | mEDAM technique Conformable derivatives Solitons Partial differential equations Density-independent DR equation Cubic nonlinearity |
| url | https://doi.org/10.1186/s13661-025-01997-w |
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