A COUPLED NONLINEAR SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS USING MODIFIED ABC OPERATOR

Hasib Khan, Jehad Alzabut, D. K. Almutairi (), Wafa Khalaf Alqurashi (), Sandra Pinelas, Osman Tun㇠and Mohammad Athar Azim ()
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Hasib Khan: Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia†Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper 18000, Khyber Pakhtunkhwa, Pakistan
Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia‡Department of Industrial Engineering, OSTİM Technical University, 06374, Ankara, Turkey§Center for Research and Innovation, Asia International University, Yangiobod MFY, G’ijduvon Street, House 74, Bukhara, Uzbekistan
D. K. Almutairi: Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952 Al-Majmaah, Saudi Arabia
Wafa Khalaf Alqurashi: Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia
Sandra Pinelas: Departamento de Ciencias Exatas e Engenharia, Academia Militar, 2720-113 Amadora, Portugal8Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Osman Tunã‡: Department of Computer Programming, Baskale Vocational School, Van Yuzuncu Yil University, Campus, 65080 Van, Turkey
Mohammad Athar Azim: 0Preparatory Year Program, College of Humanities and Sciences (CHS), Prince Sultan University, 11586 Riyadh, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-14

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

Keywords: Linearly Perturbed System; Modified ABC-Operator; Solutions and Properties; Applications of Fixed Point Theorems; Power System; Numerical Simulations; Fractal; Fractal Dimension; Fractional (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X2540105X

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