以下是使用Python编写的解决方案示例：

import datetime

def decompose_dates(start_date, end_date):
    result = {}

    # 根据月份划分
    start_month = datetime.date(start_date.year, start_date.month, 1)
    end_month = datetime.date(end_date.year, end_date.month, 1)
    while start_month <= end_month:
        month_key = start_month.strftime('%Y-%m')
        result.setdefault('按月划分', []).append(month_key)
        start_month = increment_month(start_month)

    # 根据季度划分
    start_quarter = get_quarter_start(start_date)
    end_quarter = get_quarter_start(end_date)
    while start_quarter <= end_quarter:
        quarter_key = f'Q{start_quarter.quarter} {start_quarter.year}'
        result.setdefault('按季度划分', []).append(quarter_key)
        start_quarter = increment_quarter(start_quarter)

    # 根据年份划分
    start_year = datetime.date(start_date.year, 1, 1)
    end_year = datetime.date(end_date.year, 1, 1)
    while start_year <= end_year:
        year_key = str(start_year.year)
        result.setdefault('按年份划分', []).append(year_key)
        start_year = increment_year(start_year)

    return result

def increment_month(date):
    if date.month == 12:
        return datetime.date(date.year + 1, 1, 1)
    else:
        return datetime.date(date.year, date.month + 1, 1)

def get_quarter_start(date):
    quarter_month = ((date.month - 1) // 3) * 3 + 1
    return datetime.date(date.year, quarter_month, 1)

def increment_quarter(date):
    if date.month == 10 or date.month == 7 or date.month == 4:
        return datetime.date(date.year, date.month + 3, 1)
    else:
        return datetime.date(date.year, date.month + 9, 1)

def increment_year(date):
    return datetime.date(date.year + 1, 1, 1)

# 示例用法
start_date = datetime.date(2022, 1, 15)
end_date = datetime.date(2022, 12, 31)
result = decompose_dates(start_date, end_date)
print(result)

此解决方案使用datetime库来处理日期和时间。函数decompose_dates接受开始日期和结束日期作为参数，并返回一个字典，其中包含按月、季度和年份划分的日期列表。在内部，它使用了三个辅助函数来处理月份、季度和年份的递增和划分。最后，我们提供了一个示例用法，以展示如何使用该解决方案。