In a large bowl, combine flour, cinnamon, baking powder, baking soda, and salt. Stir well.
In a separate bowl, mix together carrots, apple, raisins, applesauce, olive oil, honey, vanilla, and walnuts. Pour into dry ingredients and mix just until moistened.
Lightly spray muffin pan with olive oil cooking spray and scoop about ¼ cup batter in each muffin.