diff --git a/fastapi_limiter/__init__.py b/fastapi_limiter/__init__.py
index 2b644a2..5b48091 100644
--- a/fastapi_limiter/__init__.py
+++ b/fastapi_limiter/__init__.py
@@ -1,5 +1,5 @@
 from math import ceil
-from typing import Callable, Union
+from typing import Callable, Optional, Union
 
 from fastapi import HTTPException
 from starlette.requests import Request
@@ -46,11 +46,11 @@ async def ws_default_callback(ws: WebSocket, pexpire: int):
 
 class FastAPILimiter:
     redis = None
-    prefix: str = None
-    lua_sha: str = None
-    identifier: Callable = None
-    http_callback: Callable = None
-    ws_callback: Callable = None
+    prefix: Optional[str] = None
+    lua_sha: Optional[str] = None
+    identifier: Optional[Callable] = None
+    http_callback: Optional[Callable] = None
+    ws_callback: Optional[Callable] = None
     lua_script = """local key = KEYS[1]
 local limit = tonumber(ARGV[1])
 local expire_time = ARGV[2]
@@ -76,7 +76,7 @@ async def init(
         identifier: Callable = default_identifier,
         http_callback: Callable = http_default_callback,
         ws_callback: Callable = ws_default_callback,
-    ):
+    ) -> None:
         cls.redis = redis
         cls.prefix = prefix
         cls.identifier = identifier
@@ -85,5 +85,5 @@ async def init(
         cls.lua_sha = await redis.script_load(cls.lua_script)
 
     @classmethod
-    async def close(cls):
+    async def close(cls) -> None:
         await cls.redis.close()
diff --git a/fastapi_limiter/depends.py b/fastapi_limiter/depends.py
index 58de9f5..43fa0eb 100644
--- a/fastapi_limiter/depends.py
+++ b/fastapi_limiter/depends.py
@@ -1,6 +1,6 @@
-from typing import Callable, Optional
+from typing import Annotated, Callable, Optional
 
-from pydantic import conint
+from pydantic import Field
 from starlette.requests import Request
 from starlette.responses import Response
 from starlette.websockets import WebSocket
@@ -12,11 +12,11 @@
 class RateLimiter:
     def __init__(
         self,
-        times: conint(ge=0) = 1,
-        milliseconds: conint(ge=-1) = 0,
-        seconds: conint(ge=-1) = 0,
-        minutes: conint(ge=-1) = 0,
-        hours: conint(ge=-1) = 0,
+        times: Annotated[int, Field(ge=0)] = 1,
+        milliseconds: Annotated[int, Field(ge=-1)] = 0,
+        seconds: Annotated[int, Field(ge=-1)] = 0,
+        minutes: Annotated[int, Field(ge=-1)] = 0,
+        hours: Annotated[int, Field(ge=-1)] = 0,
         identifier: Optional[Callable] = None,
         callback: Optional[Callable] = None,
     ):