After years of blogging I purchased a domain name for my blog but after that, it got lower in the search results. how do I fix that?

Hi, Salah. 

I don't know what blogging platform you are using for your blog, but if you are now using self hosted wordpress (wordpress.org) I think by importing content from your previous blog to the new self hosted will carry all your invested content such themes, pages, postings, pictures as well as comments. I tried once, importing some postings from one self hosted wordpress to another domain with self hosted wordpress too, it carried the comments that I had in my earlier blog. 

I am not resourceful for SEO this time :) but I do think it still takes time the blog to be indexed and jump into higher search engine result. 

Thats not possible to recommend blindly. In general scenario, take care of following:

1. Work on On-Page optimization

2. Shoud have unique content that should add value for the readers.

3. For Off-page optimization, work on natural links.

The problem is that Google still relates with your content through your old domain name. So if you have changed only the domain name then there should not be much issue to get back good traffic.

You will need to make Google and all the top external links that are driving visitors to your blog aware about the change in domain name. How?

Use the301 Re-direct method. People who might have bookmarked your content/blog will be automatically taken to your site (having the new domain). The problem in this scenario is not the SEO, it is just that Google is nto aware of your domain name change.

There are other reasons too, but most probably this one should do the trick for you. If you have any query feel free to ask.