In this paper, we apply the fractional calculus and a suitable fixed point theorem with the measure of noncompactness to give the sufficient conditions of the controllability for a new class of fractional neutral integro-differential evolution systems with infinite delay and nonlocal conditions. The results are obtained here under some weakly noncompactness conditions. Thus they improve and generalize many well-known results. At the end of this paper, two examples are given to explain our abstract conclusions.
In this paper, firstly by utilizing the theory of operators semigroup, probability density functions via impulsive conditions, we establish a new PC 1−ν -mild solution for impulsive Hilfer fractional differential inclusions. Secondly we prove the existence of mild solutions for the impulsive Hilfer fractional differential inclusions by using fractional calculus, multi-valued analysis and the fixed-point technique. Then under some assumptions, the approximate controllability of associated system are formulated and proved. An example is provided to illustrate the application of the obtained theory.
This paper concerns with the existence and uniqueness of the Cauchy problem for a system of fuzzy fractional differential equation with Caputo derivative of order q∈(1,2], 0cD0+qu(t)=λu(t)⊕f(t,u(t))⊕B(t)C(t),t∈[0,T] with initial conditions u(0)=u0,u′(0)=u1. Moreover, by using direct analytic methods, the Eq–Ulam-type results are also presented. In addition, several examples are given which show the applicability of fuzzy fractional differential equations.
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