Hi Gayan,
"core muscles" is an over-used and ill-defined term in my opinion.
I am not a physio or doctor, I have however recovered from 4O years of pain by learning to use my body better by working with what I'd consider are core/key/central muscles for healthy movement.
Google images for the following 5 muscles and find them on your body. Whatever exercises you do, focus on the condition of these "5 main muscles of movement" - beginning with your "Base-Line" - and see how it feels:
Base-Line muscles:
Your pelvic floor muscles, the solid "Base" of your body. Work on being able to contract them, build the connection.
Then your rectus abdominis muscles. Your body's central "Line", from where all movement should originate. Work on activating your rectus abdominis muscles, section by section, from pelvis to chest as you breathe (in through nostrils, out through mouth) - "breathing with your Base-Line - longer and stronger with every in-breath".
You can use the midline anatomical markers of the pubic symphysis, navel and xiphoid process of sternum to increase awareness of your rectus abdominis muscles either side of midline and the linea alba.
The rectus femoris muscles of each leg align the hip and knee joints when fully activated. Think of pulling your kneecaps up to start to focus on these muscles.
The gluteus maximus muscles link the legs to Base-Line support.
The trapezius muscles from mid-back to the back of the head, shoulder to shoulder like a blanket of muscle that should be smooth and wrinkle free, guiding the head and arms through a full range of movement.
If you've questions, I'm happy to answer.
Working with these muscles has allowed me to slowly release the pain and, little by little, regain my natural range of movement.