Non-Compact Semigroups and Controllability of Fractional Evolution Equations of Order (1, 2)

This work present the controllability of fractional evolution equations of order (1, 2).We use the fractional calculus, the Monch fixed point (MFP) theorem and measure of non-compactness (MNC). A controllability result is given out for the nonlocal Cauchy problem of the fractional evolution equations including noncompact semigroups (NCSG) and the functions by excluding Lipschitz continuity. The associated theorems and properties are demonstrated in detail and an example is stated to clarify the effectiveness of the theoretical outcomes.