Murugan, M.Godavarma, C.George, S.Bate, I.Senapati, K.2026-02-032025Mathematical Modelling and Analysis, 2025, 30, 4, pp. 645-66313926292https://doi.org/10.3846/mma.2025.21979https://idr.nitk.ac.in/handle/123456789/19990In this paper, we study the convergence of a class of iterative methods for solving the system of nonlinear Banach space valued equations. We provide a unified local and semi-local convergence analysis for these methods. The convergence order of these methods are obtained using the conditions on the derivatives of the involved operator up to order 2 only. Further, we provide the number of iterations required to obtain the given accuracy of the solution. Various numerical examples including integral equations and Caputo fractional differential equations are considered to show the performance of our methods. © 2025 The Author(s). Published by Vilnius Gediminas Technical University.Banach spacesChoquet integralConvergence of numerical methodsIntegral equationsIterative methodsMathematical operatorsBasins of attractionCaputo fractional operatorConditionConvergence analysisConvergence orderFractional operatorsNumber of iterationsOrder 2Semilocal convergenceUnified approachNonlinear equations