Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM)
Several well-known nonlinear partial differential equations (NPDEs) of integer order, including the Heat Equation and the Korteweg–de Vries (KDV) Equation, as well as NPDEs of fractional order, including the fractional advection equation (FAE), fractional gas dynamic equation (FGDE), diffusion equat...
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World Scientific Publishing
2024-12-01
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| Series: | International Journal of Mathematics for Industry |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335223500119 |
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| author | Amandeep Singh Sarita Pippal |
| author_facet | Amandeep Singh Sarita Pippal |
| author_sort | Amandeep Singh |
| collection | DOAJ |
| description | Several well-known nonlinear partial differential equations (NPDEs) of integer order, including the Heat Equation and the Korteweg–de Vries (KDV) Equation, as well as NPDEs of fractional order, including the fractional advection equation (FAE), fractional gas dynamic equation (FGDE), diffusion equation, and fractional Burger equation (FBE), are approximated analytically in this study using the Shehu Transform Adomian Decomposition Method, which is a combination of two methods, namely, Shehu Transform (ST) and Adomian Decomposition Method (ADM). The Caputo sense is utilized to the fractional derivatives. This semianalytical method is used to acquire the series solutions to several example problems. The main advantage of the approach is that, in contrast to other similar semianalytical methods, it is straightforward to apply. This method has been widely used to answer any class of equations in the sciences and engineering because it can solve a huge class of linear and nonlinear equations effectively, more quickly, and precisely. The obtained solution matches exactly with the solution obtained by other methods. |
| format | Article |
| id | doaj-art-d9aeac4ae28d4f4dacb6c110ff5f34ee |
| institution | DOAJ |
| issn | 2661-3352 2661-3344 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | International Journal of Mathematics for Industry |
| spelling | doaj-art-d9aeac4ae28d4f4dacb6c110ff5f34ee2025-08-20T02:47:46ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-0116Supp0110.1142/S2661335223500119Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM)Amandeep Singh0Sarita Pippal1Department of Mathematics, Panjab University, Chandigarh, IndiaDepartment of Mathematics, Panjab University, Chandigarh, IndiaSeveral well-known nonlinear partial differential equations (NPDEs) of integer order, including the Heat Equation and the Korteweg–de Vries (KDV) Equation, as well as NPDEs of fractional order, including the fractional advection equation (FAE), fractional gas dynamic equation (FGDE), diffusion equation, and fractional Burger equation (FBE), are approximated analytically in this study using the Shehu Transform Adomian Decomposition Method, which is a combination of two methods, namely, Shehu Transform (ST) and Adomian Decomposition Method (ADM). The Caputo sense is utilized to the fractional derivatives. This semianalytical method is used to acquire the series solutions to several example problems. The main advantage of the approach is that, in contrast to other similar semianalytical methods, it is straightforward to apply. This method has been widely used to answer any class of equations in the sciences and engineering because it can solve a huge class of linear and nonlinear equations effectively, more quickly, and precisely. The obtained solution matches exactly with the solution obtained by other methods.https://www.worldscientific.com/doi/10.1142/S2661335223500119Shehu Transform (ST)Adomian Decomposition Method (ADM)Caputo operatorsFractional Partial Differential Equations (FPDEs) |
| spellingShingle | Amandeep Singh Sarita Pippal Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM) International Journal of Mathematics for Industry Shehu Transform (ST) Adomian Decomposition Method (ADM) Caputo operators Fractional Partial Differential Equations (FPDEs) |
| title | Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM) |
| title_full | Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM) |
| title_fullStr | Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM) |
| title_full_unstemmed | Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM) |
| title_short | Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM) |
| title_sort | solution of nonlinear fractional partial differential equations by shehu transform and adomian decomposition method stadm |
| topic | Shehu Transform (ST) Adomian Decomposition Method (ADM) Caputo operators Fractional Partial Differential Equations (FPDEs) |
| url | https://www.worldscientific.com/doi/10.1142/S2661335223500119 |
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