As I understand it, free will must involve some kind of self-causal agency, but I reject the concept of causality. I also don't believe in the idea of a continuous self. No one is causing the brain and the biological machine to do anything. It does as it was evolved to do.
I can give a definition of what I call volition, however. The behavior of an organism is volitional. This gives it a range of flexibility so as to make the behavior of even one well-known human-being somewhat unpredictable. This gives us an illusion of "freedom," and it can be a healthy one. But freedom is still an illusion, for the brain is acting according to the laws of physics, biochemistry, and electricity, as it has evolved to do according to natural laws. Though we cannot predict every variable of an on-coming storm, this does not make the activity of the storm exempt from natural laws of behavior. So it is with volitional behavior of an organism.
Free will seems to be grounded in the belief that free will exists or else determinism is true. I reject this. I am not a determinist. The idea of causality is an a priori assumption for which there is no proof. Yes, I understand that it is a helpful assumption in practice. The scientific method could not exist without this assumption. But philosophically speaking, this is still an assumption. As physicists learn more about the nature of time and begin to peer into the apparent lack of causality on the quantum realm and knowledge of the brain and psychology continues to increase, I begin to suspect that causality may be a result of how we perceive the world. That is, we have evolved to perceive causality, but it may be an illusion. That is not to say that it is not real, but that it is not what it seems to be. Indeed, I suspect that what exists is in reality a causal loop, not a causal chain.
And if this is the case, everything is written in stone in a causal loop, but it is not determined in the traditional sense of that word. Every event in my life simultaneously exists in different spatio-temporal locations, and whereas there is the illusion of movement, no movement is actually occurring. Time is an "eternal instance." Some of this is still highly theoretical, of course.
In any case, in order to consider questions of causality, determinism, and free will, I still have to deal with the issues of the nature of time, the nature of the self, the nature of causality, and the nature of movement.
These particular questions come to me about the nature of movement through space: How can anything possibly be moving? How can a bit of matter move through a point of infinite space? Is the fact that particles seem to disappear and reappear in different locations on the microscopic realm evidence that movement is an illusion?
All of these questions are relevant to the ideas of causality and free will. I have never come across an adequate definition of free will, and I've never read anything from legitimate scientific sources that convinced me of its existence, whatever it is.