Please see the image attached.
If it is true, how can we prove it mathematically ? otherwise, give a counterexample which demonstrate the invalidity of the proposed preposition.
I advise you to have a look at Mainardi's book on viscoelasticity or, Mainardi's exclusive articles on Mittag Lefler function (available on Arxiv too, I guess). It is strictly monotonic decreasing, but yet positive as I remember.
Use Lemma 1 of the attached paper and the result by Pollard for $E_\alpha$ that they quote in the paper.
I aslo checked the property. There is another simple way to prove. You can consider the corresponding line equation of fractional order and together with the uniquness of solution, you will derive the property by contracdition from the equation.
- Badges
- Science topic
- Similar topics
- Mathematics