Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily hig...

In this study, an innovative and sophisticated graphical tuning approach is postulated, aimed at the design of tilt-integral-derivative (TID) controllers that are specifically customized for fractional-order interval plants, whose numerators denominators consist polynomials subjected to parametric uncertainties. By leveraging powerful value set concept advanced D-composition technique, a compre...

Dialysis refers to the procedure of removing waste products and excess fluids from blood stream. This is main form treatment for both acute chronic renal failure. The need hemodialysis process optimization increasing. More than 10% adults are affected by kidney disease, it nineth leading cause deaths worldwide. Critically ill patients particularly at risk, their mortality significantly procedur...

Keywords: Fractional-order linear systems Interval uncertainty Necessary and sufficient stability condition a b s t r a c t This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix A is an interval uncertain matrix and fractional commensurate order belongs to 1 ≤ α < 2. Using the existence condition ...

In this paper, a new method is presented for synchronization between two fractional order delayed chaotic systems, while there uncertainty on the models and external disturbances enter systems at same time. The considered delay in system unspecified varied with time, of course it present different forms master slave systems. External master–slave finite manner, albeit an undetermined upper boun...