Individuals with Alzheimer's disease (AD) and Alzheimer's disease-related dementia (ADRD) experience memory and thinking changes that impact their ability to use digital daily management tools. For example, adding an event to a digital calendar requires multiple steps that may act as barriers to independent use for individuals with AD/ADRD. This paper presents AI-Care, a conversational agentic artificial intelligence (AI) layer built on top of a remote caregiving platform co-designed with people with AD/ADRD. AI-Care is designed to reduce the cognitive load on individuals with AD/ADRD when managing everyday tasks such as setting calendar reminders and organizing to-do lists through natural-language interaction with a voice-first chatbot. The system uses a LangGraph-based stateful orchestration approach in which each request passes through sanitization, intent classification, context loading, safety checks, deterministic slot collection, tool execution, and response composition. Safety-critical responses, particularly around medications and allergies, are grounded in caregiver-verified records rather than free-form model generation. The system does not make autonomous medical or treatment decisions. Incomplete or ambiguous requests are handled through controlled multi-turn clarification rather than silent failure or guessing. The system supports both typed and spoken input, with voice output through ElevenLabs text-to-speech. Longer responses are chunked before synthesis to avoid rushed playback. A preliminary pilot with four individuals with mild-to-moderate AD/ADRD showed that users found the system trustworthy, competent, and likable, and were able to complete the evaluated coordination tasks through conversation. We describe the design goals, system architecture, safety controls, and findings from this formative evaluation.