Convergence and stability analysis of fractional integral residual minimization method for fractional differential equations and system of fractional differential equations

Riyasdeen, Syed Bahurudeen; Tamilselvan, Ayyadurai; Elango, Sekar

doi:10.22124/jmm.2026.31926.2881

Convergence and stability analysis of fractional integral residual minimization method for fractional differential equations and system of fractional differential equations

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, Khadir Mohideen College, Adirampattinam, Tamil Nadu, India

² Department of Mathematics, Bharathidasan University, Tiruchirapalli, Tamil Nadu, India

³ Department of Mathematics, Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

10.22124/jmm.2026.31926.2881

Abstract

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.

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