First, fighting among siblings is very common. Many times they fighting will come in spurts. Just when you think they are getting along there will be tension and a fight erupts over what seems to be "nonsense" to an adult. At times the increase of fights signals a growth spurt in maturity of one child while another is not experiencing any significant developmental changes.
Unfortunately, with an eleven year old child you are bound to experience more challenges with sibling conflict and some tension between yourself and this child as they enter adolescence. And your seven year old will most likely seem quite irritating at times to a child entering his/her teen years. It will ebb and flow and ease in time as they both are at similar developmental stages.
Here are some resources I recommend:
There is an excellent book that I would like to recommend, Siblings Without Rivalry by Adele Faber and Elaine Mazlish. This book clearly explains the most common reasons why older children become jealous and act out when a sibling comes along. Also, strategies for coping and changing behaviors are spelled out in this book. These authors also have a companion book titled, "How to Talk So Kids Will Listen & Listen So Kids Will Talk".
Get Out of My Life, but First Could You Drive Me & Cheryl to the Mall: A Parent's Guide to the New Teenager, Revised and Updated by Anthony E. Wolf Ph.D. and Anthony E. Wolf
Lastly, there are other super resources listed on this website that I encourage you to peruse.