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Convergence and stability analysis of fractional integral residual minimization method for fractional differential equations and system of fractional differential equations | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 3، آبان 2026، صفحه 985-1004 اصل مقاله (417.44 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.31926.2881 | ||
| نویسندگان | ||
| Syed Bahurudeen Riyasdeen1؛ Ayyadurai Tamilselvan* 2؛ Sekar Elango3 | ||
| 1Department of Mathematics, Khadir Mohideen College, Adirampattinam, Tamil Nadu, India | ||
| 2Department of Mathematics, Bharathidasan University, Tiruchirapalli, Tamil Nadu, India | ||
| 3Department of Mathematics, Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India | ||
| چکیده | ||
| In this article, we propose a Fractional Integral Residual Minimization Method (FIRMM) to solve Fractional Differential Equations (FDEs) with the Caputo derivative. We provide a detailed and rigorous study of convergence analysis and stability analysis of FIRMM under suitable assumptions. Also, we extend the method FIRMM to solve a class of system of Caputo FDEs with a detailed and rigorous study on convergence analysis and stability analysis under suitable assumptions. The efficacy of our proposed method is established through numerical experiments. The advantages and limitations of FIRMM are analyzed. | ||
| کلیدواژهها | ||
| Fractional differential equations؛ semi-analytical method؛ volterra integral equations؛ special functions؛ initial value problems | ||
| مراجع | ||
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