Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience
Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering, including biosciences, neurosciences, plasma p...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
|
| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003711 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850244696127832064 |
|---|---|
| author | Md. Nur Alam Md. Azizur Rahman |
| author_facet | Md. Nur Alam Md. Azizur Rahman |
| author_sort | Md. Nur Alam |
| collection | DOAJ |
| description | Time-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering, including biosciences, neurosciences, plasma physics, geochemistry, and fluid mechanics. In this context, we examine the time-space fractional soliton neuron model (TSFSNM), which holds significant importance in neuroscience. This model explains how action potentials are initiated and propagated by axons, based on a thermodynamic theory of nerve pulse transmission. The signals passing through the cell membrane (CM) are proposed to take the form of solitary sound pulses, which can be represented as solitons. To investigate these soliton solutions, nonlinear fractional differential equations (NLFDEs) are transformed into corresponding partial differential equations (PDEs) using a fractional complex transform (FCT). The Kudryashov method is then applied to determine the wave profiles for the TSFSNM equation. We present 3D, 2D, contour, and density plots of the TSFSNM equation, and further analyze how fractional and time-space parameters influence these wave profiles through additional graphical representations. Kink, singular kink and different types of soliton solutions are successfully recovered through the Kudryashov method. The outcomes of various studies show that the applied method is highly efficient and well-suited for tackling problems in applied sciences and mathematical physics. Graphical representations, coupled with numerical data, reinforce the validity and accuracy of the technique. The proposed method is a convenient and powerful tool for handling the solution of nonlinear equations, making it particularly effective in exploring complex wave phenomena in diverse scientific fields. |
| format | Article |
| id | doaj-art-ccf2fb4747b4497e85e12e42aeb31de3 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-ccf2fb4747b4497e85e12e42aeb31de32025-08-20T01:59:39ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210098510.1016/j.padiff.2024.100985Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscienceMd. Nur Alam0Md. Azizur Rahman1Corresponding author.; Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, BangladeshDepartment of Mathematics, Pabna University of Science and Technology, Pabna 6600, BangladeshTime-space fractional nonlinear problems (T-SFNLPs) play a crucial role in the study of nonlinear wave propagation. Time-space nonlinearity is prevalent across various fields of applied science, nonlinear dynamics, mathematical physics, and engineering, including biosciences, neurosciences, plasma physics, geochemistry, and fluid mechanics. In this context, we examine the time-space fractional soliton neuron model (TSFSNM), which holds significant importance in neuroscience. This model explains how action potentials are initiated and propagated by axons, based on a thermodynamic theory of nerve pulse transmission. The signals passing through the cell membrane (CM) are proposed to take the form of solitary sound pulses, which can be represented as solitons. To investigate these soliton solutions, nonlinear fractional differential equations (NLFDEs) are transformed into corresponding partial differential equations (PDEs) using a fractional complex transform (FCT). The Kudryashov method is then applied to determine the wave profiles for the TSFSNM equation. We present 3D, 2D, contour, and density plots of the TSFSNM equation, and further analyze how fractional and time-space parameters influence these wave profiles through additional graphical representations. Kink, singular kink and different types of soliton solutions are successfully recovered through the Kudryashov method. The outcomes of various studies show that the applied method is highly efficient and well-suited for tackling problems in applied sciences and mathematical physics. Graphical representations, coupled with numerical data, reinforce the validity and accuracy of the technique. The proposed method is a convenient and powerful tool for handling the solution of nonlinear equations, making it particularly effective in exploring complex wave phenomena in diverse scientific fields.http://www.sciencedirect.com/science/article/pii/S266681812400371135E0535C0835Q5137L5037J2533F05 |
| spellingShingle | Md. Nur Alam Md. Azizur Rahman Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience Partial Differential Equations in Applied Mathematics 35E05 35C08 35Q51 37L50 37J25 33F05 |
| title | Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience |
| title_full | Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience |
| title_fullStr | Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience |
| title_full_unstemmed | Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience |
| title_short | Study of the parametric effect of the wave profiles of the time-space fractional soliton neuron model equation arising in the topic of neuroscience |
| title_sort | study of the parametric effect of the wave profiles of the time space fractional soliton neuron model equation arising in the topic of neuroscience |
| topic | 35E05 35C08 35Q51 37L50 37J25 33F05 |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003711 |
| work_keys_str_mv | AT mdnuralam studyoftheparametriceffectofthewaveprofilesofthetimespacefractionalsolitonneuronmodelequationarisinginthetopicofneuroscience AT mdazizurrahman studyoftheparametriceffectofthewaveprofilesofthetimespacefractionalsolitonneuronmodelequationarisinginthetopicofneuroscience |