A COUPLED NONLINEAR SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS USING MODIFIED ABC OPERATOR
Hasib KhanDepartment of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi ArabiaJehad AlzabutCenter for Research and Innovation, Asia International University, Yangiobod MFY, G’ijduvon Street, House 74, Bukhara, UzbekistanD. K. AlmutairiDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952 Al-Majmaah, Saudi ArabiaWafa AlqurashiDepartment of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi ArabiaSandra PinelasCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalOsman TunçDepartment of Computer Programming, Baskale Vocational School, Van Yuzuncu Yil University, Campus, 65080 Van, TurkeyMOHAMMAD ATHAR AZIMPreparatory Year Program, College of Humanities and Sciences (CHS), Prince Sultan University, 11586 Riyadh, Saudi Arabia
ABI
Abstract
This 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 approaches
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