Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique
The primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditions. Our proposed approach, the Multistage Telescoping Decomp...
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MDPI AG
2025-03-01
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| author | Mohammed Boukedroun Souad Ayadi Fouzia Chita Meltem Erden Ege Ozgur Ege Rajagopalan Ramaswamy |
| author_facet | Mohammed Boukedroun Souad Ayadi Fouzia Chita Meltem Erden Ege Ozgur Ege Rajagopalan Ramaswamy |
| author_sort | Mohammed Boukedroun |
| collection | DOAJ |
| description | The primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditions. Our proposed approach, the Multistage Telescoping Decomposition Elzaki Method (MTDEM), integrates the advantages of the Elzaki transform with the Multistage Telescoping Decomposition Method (MTDM), significantly enhancing the efficiency of the solution process and improving the convergence rate. Additionally, it simplifies computational operations and reduces the computational complexity associated with solving these nonlinear systems. A comprehensive comparison is conducted to highlight the accuracy and computational advantages of our proposed method compared to existing techniques, including the exact solution and the Telescoping Decomposition Method (TDM), through numerical examples that demonstrate the effectiveness of the proposed approach. The flexibility of the MTDEM allows for its application in a wide range of nonlinear SFDEs, making it a valuable tool in various scientific and engineering fields. These systems are widely used in modeling numerous physical, biological, and economic phenomena, such as the dynamics of electrical systems, heat transfer, and population growth models, underscoring the importance of developing accurate and efficient computational methods for their solutions. Through this study, we present a novel contribution to enhancing numerical and analytical techniques, paving the way for broader applications in multiple domains that require precise and reliable solutions for complex fractional systems. |
| format | Article |
| id | doaj-art-e116c504d0704a039d3906cc95f44b63 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-e116c504d0704a039d3906cc95f44b632025-08-20T02:17:14ZengMDPI AGAxioms2075-16802025-03-0114423310.3390/axioms14040233Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical TechniqueMohammed Boukedroun0Souad Ayadi1Fouzia Chita2Meltem Erden Ege3Ozgur Ege4Rajagopalan Ramaswamy5Department of Mathematics, Khemis Miliana University, Ain Defla 44225, AlgeriaAcoustics and Civil Engineering Laboratory, Department of Material Sciences, Khemis Miliana University, Ain Defla 44225, AlgeriaDepartment of Mathematics, Khemis Miliana University, Ain Defla 44225, AlgeriaIndependent Researcher, 35000 Izmir, TurkeyDepartment of Mathematics, Ege University, 35100 Izmir, TurkeyDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi ArabiaThe primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditions. Our proposed approach, the Multistage Telescoping Decomposition Elzaki Method (MTDEM), integrates the advantages of the Elzaki transform with the Multistage Telescoping Decomposition Method (MTDM), significantly enhancing the efficiency of the solution process and improving the convergence rate. Additionally, it simplifies computational operations and reduces the computational complexity associated with solving these nonlinear systems. A comprehensive comparison is conducted to highlight the accuracy and computational advantages of our proposed method compared to existing techniques, including the exact solution and the Telescoping Decomposition Method (TDM), through numerical examples that demonstrate the effectiveness of the proposed approach. The flexibility of the MTDEM allows for its application in a wide range of nonlinear SFDEs, making it a valuable tool in various scientific and engineering fields. These systems are widely used in modeling numerous physical, biological, and economic phenomena, such as the dynamics of electrical systems, heat transfer, and population growth models, underscoring the importance of developing accurate and efficient computational methods for their solutions. Through this study, we present a novel contribution to enhancing numerical and analytical techniques, paving the way for broader applications in multiple domains that require precise and reliable solutions for complex fractional systems.https://www.mdpi.com/2075-1680/14/4/233nonlinear systemnumerical techniqueElzaki transformfractional-order equationsCaputo derivatives |
| spellingShingle | Mohammed Boukedroun Souad Ayadi Fouzia Chita Meltem Erden Ege Ozgur Ege Rajagopalan Ramaswamy Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique Axioms nonlinear system numerical technique Elzaki transform fractional-order equations Caputo derivatives |
| title | Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique |
| title_full | Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique |
| title_fullStr | Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique |
| title_full_unstemmed | Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique |
| title_short | Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique |
| title_sort | solutions of nonlinear fractional order differential equation systems using a numerical technique |
| topic | nonlinear system numerical technique Elzaki transform fractional-order equations Caputo derivatives |
| url | https://www.mdpi.com/2075-1680/14/4/233 |
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