Local Existence and Regularity of Solutions in α-norm for Some Second Order Partial Neutral Functional Differential Equations with Infinite Delay

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Résumé

This work examines the existence and regularity of solutions in the alpha-norm for second order partial neutral functional differential equations with infinite delay in Banach spaces. To establish the local existence of solutions, we use the cosine families theory and Schauder’s fixed point theorem. We also provide sufficient conditions to ensure solution regularity. Finally, we present an example to illustrate the theoretical results.

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