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Mathematical analysis demonstrates local existence and well-posedness for abstract integro-differential equations, suggesting broad utility in modeling complex population dynamics.
We develop a framework for abstract integro‐differential equations with state‐dependent integration intervals and demonstrate its applicability to partial differential equations. Using Banach's contraction principle and the Schauder fixed‐point theorem, we prove local existence and uniqueness and establish local well‐posedness for both mild and strict solutions. The paper concludes with examples drawn from population dynamics that illustrate the theory.
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Pandey et al. (2026) studied this question.
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