2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations
| Format: | General Document |
|---|
| _version_ | 1860798332418392064 |
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| building | INTELEK Repository |
| collection | Online Access |
| collectionurl | https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 |
| copyright | Copyright©PWB2025 |
| country | Malaysia |
| date | 2025-04-09 17:13 |
| format | General Document |
| id | 17254 |
| institution | UniSZA |
| originalfilename | INCORPORATING FUZZINESS IN THE RESIDUAL POWER SERIES AND REPRODUCING KERNEL HILBERT SPACE METHODS FOR FUZZY FRACTIONAL RICCATI EQUATIONS (PHD_025) (1).pdf |
| person | Moath Ali Alshorman |
| recordtype | oai_dc |
| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=17254 |
| sourcemedia | Server storage Scanned document |
| spelling | 17254 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=17254 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection3 General Document Malaysia Library Staff (Top Management) Library Staff (Management) Library Staff (Support) Terengganu Faculty of Informatics & Computing English application/pdf 1.5 147 Microsoft® Word 2010 Server storage Scanned document UniSZA Private Access UniSZA Copyright©PWB2025 UniSZA Dissertations-Academic Moath Ali Alshorman Differential Equations—Fractional Calculus Algorithms—Mathematical models Nuclear Decay—Mathematical Models Applied Mathematics Fuzzy Fractional Differential Equations Fuzzy Fractional Riccati Equations Residual Power Series Method (RPSM) Reproducing Kernel Hilbert Space Method (RKHSM) Caputo Derivative Numerical Methods 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations Riccati Equations are one of the important forms of differential equations that have many important applications in various sciences and engineering, as the presence of fuzzy and fractional orders transforms these equations into Fuzzy Fractional Riccati Equations (FFREs) and expands the fields of applications of these equations in engineering and other sciences. Previous research indicates a clear lack of solutions to these equations, which limits their applications. Therefore, this study aims to develop a new approach to solve FFREs using the Residual Power Series Method (RPSM) and also to develop a new approach to solve FFREs using Reproducing Kernel Hilbert Space Method (RKHSM), as well as to test the effectiveness and accuracy of the developed methods by developing them in the form of algorithms and applied examples, as well as using appropriate software, which contributes to expanding the scope of applications. The methodology of this study is based first on formulating the Riccati Equations by integrating fuzzy values and fractional differential orders, which is usually achieved by using mathematical definitions of fuzzy values, such as trigonometric and trapezoidal fuzzy numbers, not to mention using the definitions given by Caputo and Riemann–Liouville. Therefore, the steps to solve these equations involve modifying and developing the RPSM to accommodate the presence of fuzzy values and fractional differential orders. In addition, the steps of RKHSM are adapted, modified and developed to accommodate the inclusion of fuzzy values and differential orders, and then these developed methods are formulated as algorithms, and their effectiveness is finally tested through several applied examples, where the results reveal the mathematical formulas of these equations including fuzzy and fractional elements. Moreover, these equations become more comprehensive when including fuzzy values and fractional order. The results include the development of these methods for solving equations using RPSM and the RKHSM. Algorithms were employed to implement solutions, examples were solved using the two new methods, comparisons were made, the effectiveness of the new methodology was verified, where β ∈ [0,1], and the application of this methodology to equations used in nuclear decay was explored. The objectives of this study were achieved by formulating new methods for solving FFREs using RPSM and RKHSM and their effectiveness was verified through mathematical examples and comparison, demonstrating the accuracy and convergence of the solutions. These new methods also proved their effectiveness in solving the nuclear decay equation, taking into account the effect of ambiguity in its values and fractional orders, which is evident from the convergence of the solutions compared to the Variational Iteration Method. 2025-04-09 17:13 uuid:fabdabee-cd2c-474d-bec7-37c7b0db8b6d INCORPORATING FUZZINESS IN THE RESIDUAL POWER SERIES AND REPRODUCING KERNEL HILBERT SPACE METHODS FOR FUZZY FRACTIONAL RICCATI EQUATIONS (PHD_025) (1).pdf Thesis |
| spellingShingle | 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations |
| state | Terengganu |
| subject | Dissertations-Academic Differential Equations—Fractional Calculus Algorithms—Mathematical models Nuclear Decay—Mathematical Models Applied Mathematics |
| summary | Riccati Equations are one of the important forms of differential equations that have many important applications in various sciences and engineering, as the presence of fuzzy and fractional orders transforms these equations into Fuzzy Fractional Riccati Equations (FFREs) and expands the fields of applications of these equations in engineering and other sciences. Previous research indicates a clear lack of solutions to these equations, which limits their applications. Therefore, this study aims to develop a new approach to solve FFREs using the Residual Power Series Method (RPSM) and also to develop a new approach to solve FFREs using Reproducing Kernel Hilbert Space Method (RKHSM), as well as to test the effectiveness and accuracy of the developed methods by developing them in the form of algorithms and applied examples, as well as using appropriate software, which contributes to expanding the scope of applications. The methodology of this study is based first on formulating the Riccati Equations by integrating fuzzy values and fractional differential orders, which is usually achieved by using mathematical definitions of fuzzy values, such as trigonometric and trapezoidal fuzzy numbers, not to mention using the definitions given by Caputo and Riemann–Liouville. Therefore, the steps to solve these equations involve modifying and developing the RPSM to accommodate the presence of fuzzy values and fractional differential orders. In addition, the steps of RKHSM are adapted, modified and developed to accommodate the inclusion of fuzzy values and differential orders, and then these developed methods are formulated as algorithms, and their effectiveness is finally tested through several applied examples, where the results reveal the mathematical formulas of these equations including fuzzy and fractional elements. Moreover, these equations become more comprehensive when including fuzzy values and fractional order. The results include the development of these methods for solving equations using RPSM and the RKHSM. Algorithms were employed to implement solutions, examples were solved using the two new methods, comparisons were made, the effectiveness of the new methodology was verified, where β ∈ [0,1], and the application of this methodology to equations used in nuclear decay was explored. The objectives of this study were achieved by formulating new methods for solving FFREs using RPSM and RKHSM and their effectiveness was verified through mathematical examples and comparison, demonstrating the accuracy and convergence of the solutions. These new methods also proved their effectiveness in solving the nuclear decay equation, taking into account the effect of ambiguity in its values and fractional orders, which is evident from the convergence of the solutions compared to the Variational Iteration Method. |
| title | 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations |
| title_full | 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations |
| title_fullStr | 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations |
| title_full_unstemmed | 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations |
| title_short | 2025_Incorporating Fuzziness In The Residual Power Series And Reproducing Kernel Hilbert Space Methods For Fuzzy Fractional Riccati Equations |
| title_sort | 2025_incorporating fuzziness in the residual power series and reproducing kernel hilbert space methods for fuzzy fractional riccati equations |