Khan, HasibAlzabut, JehadAlmutairi, D. K.Alqurashi, Wafa khalafPinelas, SandraTunc, OsmanAzim, Mohammad athar2025-05-102025-05-1020250218-348X1793-654310.1142/S0218348X2540105X2-s2.0-105001577794https://doi.org/10.1142/S0218348X2540105Xhttps://hdl.handle.net/20.500.14720/12347Azim, Mohammad Athar/0009-0003-5342-1765; Khan, Hasib/0000-0002-7186-8435; Tunc, Osman/0000-0003-2965-4561This paper explores the necessary conditions required for the solutions of an integro-differential system of n-fractional differential equations (n-FDEs) in the modified-ABC case of derivative with initial conditions. The presumed problem is a linearly perturbed system. Some classical fixed point theorems are utilized to derive the solution existence criteria. Additionally, a numerical methodology utilizing Lagrange's interpolation polynomial is developed and implemented in a dynamical framework of a power system for practical applications. In addition, we investigate the properties of Hyers-Ulam's stability and uniqueness. The findings are evaluated using graphical methods to assess the precision and suitability of the approacheseninfo:eu-repo/semantics/closedAccessLinearly Perturbed SystemModified Abc-OperatorSolutions And PropertiesApplications Of Fixed Point TheoremsPower SystemNumerical SimulationsFractalFractal DimensionFractionalArticleN/AQ1WOS:001455324700001