Novel criteria for existence and stability in nonlocal fractional symmetric hahn integro-difference boundary problems
Keywords:
Fractional symmetric Hahn integral, Riemann-Liouville fractional symmetric Hahn difference, nonlocal boundary value problems, existence, Hyers-Ulam stabilityAbstract
This article pioneers the study of a highly intricate nonlocal boundary value problem within the framework of fractional symmetric Hahn integro-difference calculus. The novel formulation is defined by an unprecedented structure, simultaneously incorporating four fractional symmetric Hahn difference operators of distinct orders alongside an auxiliary fractional symmetric Hahn integral. This unique configuration presents significant structural challenges that necessitate advanced analytical techniques. We establish rigorous existence and uniqueness results for the proposed problem by effectively leveraging the Banach contraction principle and Schauder’s fixed point theorem. Furthermore, the robustness of the derived solutions is thoroughly investigated via a comprehensive Hyers–Ulam stability analysis. To support this analysis, several essential, previously underexplored properties of the fractional symmetric Hahn integral are established and meticulously applied. Our findings not only represent a substantial contribution to the nascent field of fractional discrete calculus but also provide a crucial theoretical foundation for the modeling and analysis of complex, nonlocal dynamical systems.
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