Qualitative Analysis of Positive Solutions for Coupled Atangana-Baleanu-Caputo Fractional Systems with Nonlocal Integral Conditions

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DOI: https://doi.org/10.28924/2291-8639-24-2026-315
Published: Oct 5, 2026
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Selvakumar Viswanathan, Jeyachandhiran Ramaprabu, Gunaseelan Mani, Fady Hasan, Nabil Mlaiki, Qualitative Analysis of Positive Solutions for Coupled Atangana-Baleanu-Caputo Fractional Systems with Nonlocal Integral Conditions, Int. J. Anal. Appl., 24 (2026), 315.

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Selvakumar Viswanathan, Jeyachandhiran Ramaprabu, Gunaseelan Mani, Fady Hasan, Nabil Mlaiki

Abstract

This article investigates a coupled system of nonlinear FDEs involving the \(\mathsf{ABC}\) fractional derivative with IBCs. By employing the upper and lower solution approach in conjunction with Schauder's FPT, we establish existence of positive solutions without imposing any monotonicity restrictions on the nonlinear terms. The uniqueness of solution is demonstrated via the Banach contraction principle under suitable Lipschitz conditions. Furthermore, we analyze the stability properties of the obtained solutions using the concepts of Ulam-Hyers (UH), Generalized UH (GUH) and UH-Rassias (UHR) stability. Two numerical examples are provided to illustrate theoretical results. The proposed framework is particularly useful for handling non-monotone nonlinearities in coupled \(\mathsf{ABC}\) fractional systems with nonlocal boundary conditions.

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