Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative
In the present work, a relatively new derivative namely the Atangana–Baleanu fractional derivative is extended to derive an approximate solution to the non-linear higher dimensional fractional differential equations such as the Fractional perturbed Zakharov–Kuznetsov equation. The said model arises...
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Elsevier
2025-03-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S259012302500204X |
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| author | Attiya Nazneen Rashid Nawaz Laiq Zada Nasir Ali Mohamed Benghanem Hijaz Ahmad |
| author_facet | Attiya Nazneen Rashid Nawaz Laiq Zada Nasir Ali Mohamed Benghanem Hijaz Ahmad |
| author_sort | Attiya Nazneen |
| collection | DOAJ |
| description | In the present work, a relatively new derivative namely the Atangana–Baleanu fractional derivative is extended to derive an approximate solution to the non-linear higher dimensional fractional differential equations such as the Fractional perturbed Zakharov–Kuznetsov equation. The said model arises in many fields of physics and mathematics to model the dust-ion-acoustic waves in the magnetized two ion-temperature in the dusty plasmas. The methodology used for the simulation of the above model is the Adomian decomposition method and the derivative is considered as the Atangana–Baleanu fractional derivative in the Caputo's sense. The method has been successfully applied to the higher dimension fractional order Partial differential equations and some fruitful results have been achieved. The combination handles these types of equations appropriately and simply. The devised method yields the best approximate solutions shown numerically and graphically through tables and graphs respectively. Comparison of the absolute errors for different fractional orders confirms the efficiency, precision and convergence of the proposed method towards an exact solution in a few iterations. |
| format | Article |
| id | doaj-art-12b69db8f2b24b2a8e75b85106b3f819 |
| institution | Kabale University |
| issn | 2590-1230 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Engineering |
| spelling | doaj-art-12b69db8f2b24b2a8e75b85106b3f8192025-02-09T05:01:03ZengElsevierResults in Engineering2590-12302025-03-0125104116Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivativeAttiya Nazneen0Rashid Nawaz1Laiq Zada2Nasir Ali3Mohamed Benghanem4Hijaz Ahmad5Department of Mathematics, Abdul Wali Khan University Mardan, KP, 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, KP, 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, KP, 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, KP, 23200, PakistanPhysics Department, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia; Corresponding author.Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey; Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, 42351, Saudi Arabia; Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, South Korea; Department of Technical Sciences, Western Caspian University, Baku, 1001, AzerbaijanIn the present work, a relatively new derivative namely the Atangana–Baleanu fractional derivative is extended to derive an approximate solution to the non-linear higher dimensional fractional differential equations such as the Fractional perturbed Zakharov–Kuznetsov equation. The said model arises in many fields of physics and mathematics to model the dust-ion-acoustic waves in the magnetized two ion-temperature in the dusty plasmas. The methodology used for the simulation of the above model is the Adomian decomposition method and the derivative is considered as the Atangana–Baleanu fractional derivative in the Caputo's sense. The method has been successfully applied to the higher dimension fractional order Partial differential equations and some fruitful results have been achieved. The combination handles these types of equations appropriately and simply. The devised method yields the best approximate solutions shown numerically and graphically through tables and graphs respectively. Comparison of the absolute errors for different fractional orders confirms the efficiency, precision and convergence of the proposed method towards an exact solution in a few iterations.http://www.sciencedirect.com/science/article/pii/S259012302500204XAdomian decomposition method (ADM)Fractional order generalized perturbed zakharov–kuznetsov (FGPZK) equationExact solution |
| spellingShingle | Attiya Nazneen Rashid Nawaz Laiq Zada Nasir Ali Mohamed Benghanem Hijaz Ahmad Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative Results in Engineering Adomian decomposition method (ADM) Fractional order generalized perturbed zakharov–kuznetsov (FGPZK) equation Exact solution |
| title | Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative |
| title_full | Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative |
| title_fullStr | Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative |
| title_full_unstemmed | Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative |
| title_short | Analysis of the non-linear higher dimensional fractional differential equations arising in dusty plasma using the Atangana–Baleanu fractional derivative |
| title_sort | analysis of the non linear higher dimensional fractional differential equations arising in dusty plasma using the atangana baleanu fractional derivative |
| topic | Adomian decomposition method (ADM) Fractional order generalized perturbed zakharov–kuznetsov (FGPZK) equation Exact solution |
| url | http://www.sciencedirect.com/science/article/pii/S259012302500204X |
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