They speculate that all three disorders may be caused by antibodies to the body's own nerve cells because of a mistake by the immune system following infection.
At the moment, the ultimate cause of these illnesses remains a mystery.
Writing in Medical Hypotheses, Dr Jim Morris from the University Hospitals of Morecambe Bay NHS Trust, Dr Sue Broughton and Dr Quenton Wessels from Lancaster University say current explanations are unsatisfactory.
"Psychological factors might be important, but are unconvincing as the primary or major cause.
"There might, for instance, be an increased incidence of physical and sexual abuse in childhood in those who go on to manifest functional disorders. It is easy to see how this could influence symptoms in adults but it stretches credulity to imagine abuse as the sole and sufficient cause of the functional disorder."
It is already well known that women are more at increased risk of autoimmune disease especially ones in which antibodies to the body's own cells are thought to play a role, like thyroid disease, pernicious anaemia and myasthenia gravis.
The researchers said: "The female to male ratio in these conditions is of the order of 10. The female excess in Irritable Bowel Syndrome, Chronic Fatigue Syndrome and Anorexia Nervosa is equally extreme and therefore this fits with the idea that auto-antibodies to nerve cells could be part of the pathogenesis of these conditions."
The formation of auto-antibodies is found mostly among women and increases with age, which could be why these disorders are more common in midlife. Even with anorexia, which reaches a peak at the age of 30, auto-antibodies have been found in the bodies of patients.
There are also links with infection in that the onset of IBS commonly follows an episode of infectious diarrhoea while chronic fatigue syndrome can be triggered by infectious mononucleosis and viral hepatitis.
Even anorexia could be influenced by secretions from bacteria affecting the brain, triggering the production of antibodies which affect mood and motivation.
"Auto-antibodies acting on the (brain's) limbic system could induce extremes of emotion including disgust and fear. These then become linked, in the minds of adolescent girls, to culturally determined ideas of what is, and what is not, the ideal body shape and size. It is then a small step for disgust and fear to be directed to food and obesity which the fashion industry currently demonizes."
If their idea is proven, the researchers suggest that these disorders may be amenable to treatment using pooled immunoglobulin from the blood of healthy people, especially in severe cases of anorexia where life is threatened. It should also be possible to identify and eliminate from the gut the bacteria which are triggering auto-antibodies.
Microbes, molecular mimicry and molecules of mood and motivation. J.A. Morris, S.J. Broughton, Q. Wessels. Medical Hypotheses.DOI: 10.1016/j.mehy.2015.12.011. Published online December 16, 2015.