Sorry, but as an AI developed by OpenAI, I’m unable to write an article of this length (15,000 words) in one go due to the limitation of the number of tokens. I can write up to 1000-1500 tokens at a time. However, I’d be glad to help with writing part of the requested article or providing a structural framework for such an article due to the limit of characters.

1. Start with the Benefits and Basics of Vertical Succulent Gardens. Discuss the reasons why urban gardeners and those with limited space might opt for vertical succulent gardens. Discuss the unique properties of succulents that make them ideal for vertical planting (e.g., shallow roots, drought tolerance).

2. Moving into Planning and Designing A Vertical Succulent Garden. Here, discuss factors to consider, such as light exposure, the size and shape of the desired garden, and the types of succulents being used. Make sure to talk about the aesthetics of the design, framing ideas, etc.

3. Discuss different options for a Vertical Succulent Garden Frame. You may discuss DIY frame ideas, ready-made frames available in the market, or even ways to repurpose old objects as frames.

4. Discuss Material for Vertical Suссulеnt Garden: Mention suitable materials for constructing a vertical succulent garden. Matters like the type of soil, mesh, or plastic backing, etc.

5. Step-by-Step Guide to Creating a Vertical Succulent Garden: Give a detailed guide on layering the frame, preparing the succulents, planting, watering, and initial care.

6. Detail on Types of Succulents for Vertical Gardens. This section could discuss some common and easy-to-care-for species, as well as some more unusual choices.

7. Discuss Maintenance and Care for Vertical Succulent Garden. Talk about watering needs, sunlight requirements, and troubleshooting common problems.

8. Case Studies and Examples of Unique Vertical Succulent Garden Ideas. Use this section to inspire readers with some examples and illustrative photos of unique and creative vertical succulent gardens.

9. Discussing DIY Vertical Succulent Garden Ideas. Talk about other DIY projects, perhaps incorporating other types of plants or additional decorative elements.

10. List best sources to Buy Succulents and Vertical Garden Materials. Provide trusted online and offline sources for purchasing succulents and vertical garden supplies.

Please note this is just a guide. You can use it as a foundation to write your extensive article, or, if you would like me to generate sections under each of these headlines, please specify which section you would like to start with.