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Theoretical analysis demonstrates existence and multiplicity of solutions in discrete fractional boundary systems, indicating rigorous criteria for mixed-order nabla operators.
In this manuscript, we study the solvability of a class of mixed-order nabla fractional equations coupled with Dirichlet conditions. Based on the obtained Green’s function and its properties, we establish existence, nonexistence, and multiplicity results using fixed point theory. In the end, we give some numerical examples that verify our theoretical results.
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Dimitrov et al. (2026) studied this question.
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