Implementation of Yang residual power series method to solve fractional non-linear systems
In this study, we implemented the Yang residual power series (YRPS) methodology, a unique analytical treatment method, to estimate the solutions of a non-linear system of fractional partial differential equations. The RPS approach and the Yang transform are togethered in the YRPS method. The suggest...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023418?viewType=HTML |
| _version_ | 1797905408191365120 |
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| author | Azzh Saad Alshehry Roman Ullah Nehad Ali Shah Rasool Shah Kamsing Nonlaopon |
| author_facet | Azzh Saad Alshehry Roman Ullah Nehad Ali Shah Rasool Shah Kamsing Nonlaopon |
| author_sort | Azzh Saad Alshehry |
| collection | DOAJ |
| description | In this study, we implemented the Yang residual power series (YRPS) methodology, a unique analytical treatment method, to estimate the solutions of a non-linear system of fractional partial differential equations. The RPS approach and the Yang transform are togethered in the YRPS method. The suggested approach to handle fractional systems is explained along with its application. With fewer calculations and greater accuracy, the limit idea is used to solve it in Yang space to produce the YRPS solution for the proposed systems. The benefit of the new method is that it requires less computation to get a power series form solution, whose coefficients should be established in a series of algebraic steps. Two attractive initial value problems were used to test the technique's applicability and performance. The behaviour of the approximative solutions is numerically and visually discussed, along with the effect of fraction order ς. It was observed that the proposed method's approximations and exact solutions were completely in good agreement. The YRPS approach results highlight and show that the approach may be utilized to a variety of fractional models of physical processes easily and with analytical efficiency. |
| first_indexed | 2024-04-10T10:05:54Z |
| format | Article |
| id | doaj.art-9752f8a697ae4ef4874637b38606ae71 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T10:05:54Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-9752f8a697ae4ef4874637b38606ae712023-02-16T01:16:07ZengAIMS PressAIMS Mathematics2473-69882023-02-01848294830910.3934/math.2023418Implementation of Yang residual power series method to solve fractional non-linear systemsAzzh Saad Alshehry0Roman Ullah1Nehad Ali Shah2Rasool Shah3Kamsing Nonlaopon41. Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia2. Department of General Studies, Higher Colleges of Technology, Dubai Women Campus, UAE3. Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea4. Department of Mathematics, Abdul Wali khan University Mardan 23200, Pakistan5. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandIn this study, we implemented the Yang residual power series (YRPS) methodology, a unique analytical treatment method, to estimate the solutions of a non-linear system of fractional partial differential equations. The RPS approach and the Yang transform are togethered in the YRPS method. The suggested approach to handle fractional systems is explained along with its application. With fewer calculations and greater accuracy, the limit idea is used to solve it in Yang space to produce the YRPS solution for the proposed systems. The benefit of the new method is that it requires less computation to get a power series form solution, whose coefficients should be established in a series of algebraic steps. Two attractive initial value problems were used to test the technique's applicability and performance. The behaviour of the approximative solutions is numerically and visually discussed, along with the effect of fraction order ς. It was observed that the proposed method's approximations and exact solutions were completely in good agreement. The YRPS approach results highlight and show that the approach may be utilized to a variety of fractional models of physical processes easily and with analytical efficiency.https://www.aimspress.com/article/doi/10.3934/math.2023418?viewType=HTMLyang transformcaputo operatorresidual power seriessystems of fractional differential equations |
| spellingShingle | Azzh Saad Alshehry Roman Ullah Nehad Ali Shah Rasool Shah Kamsing Nonlaopon Implementation of Yang residual power series method to solve fractional non-linear systems AIMS Mathematics yang transform caputo operator residual power series systems of fractional differential equations |
| title | Implementation of Yang residual power series method to solve fractional non-linear systems |
| title_full | Implementation of Yang residual power series method to solve fractional non-linear systems |
| title_fullStr | Implementation of Yang residual power series method to solve fractional non-linear systems |
| title_full_unstemmed | Implementation of Yang residual power series method to solve fractional non-linear systems |
| title_short | Implementation of Yang residual power series method to solve fractional non-linear systems |
| title_sort | implementation of yang residual power series method to solve fractional non linear systems |
| topic | yang transform caputo operator residual power series systems of fractional differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023418?viewType=HTML |
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