Abstract
In this paper, we consider the finite approximate controllability of some Hilfer fractional evolution systems. Using a variational approach and Schauder’s fixed point theorem, we give sufficient conditions for finite approximate controllability of semilinear controlled systems. An example is given to illustrate our theory.
Highlights
1 Introduction In this paper, we investigate the Hilfer fractional evolution system: D0ν+,μx(t) = Ax(t) + f (t, x(t)) + Bu(t), t ∈ J = (0, b], I0(1+–ν)(1–μ)x(0) = x0, (1.1)
(2020) 2020:22 of fractional evolution equations involving Hilfer fractional derivatives was considered and in [14], we study the approximate controllability of Hilfer fractional evolution hemivariational inequalities by two resolvent operators and fixed point theorem
4 Finite approximate controllability for the semilinear case we study the finite approximate controllability of system (1.1)
Summary
The admissible controls set U is a Hilbert space, B is a bounded linear operator from Nonexistence, uniqueness involving Hilfer fractional derivatives was discussed in [10,11,12] and in [13] the approximate controllability Definition 2.2 The right-side Riemann–Liouville fractional derivative of order α ∈ (n – 1, n), n ∈ Z+ for a function f : [a, ∞) → E is defined by
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