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2020
DOI: 10.18514/mmn.2020.2921
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Finite approximate controllability of Hilfer fractional semilinear differential equations

Abstract: In this paper, we investigate the finite approximate controllability of fractional semilinear differential equations involving the Hilfer derivative. We show that if the linear part is approximate controllable, then under suitable conditions the semilinear system is finite approximate controllable.

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Cited by 11 publications
(6 citation statements)
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“…Definition 5 (Approximate Controllability [39]). System ( 1) is called approximately controllable on [0, τ] if, for every φ ∈ C([−h, 0]; Z), ς 1 ∈ P C(I, Z), and ≥ 0, there exists ṽ ∈ P C(I, U) such that the corresponding solution ς(µ) of (1) satisfies ς(0) = φ(0) and ς(τ) − ς 1 Z ≤ .…”
Section: Lemma 2 ([38]mentioning
confidence: 99%
“…Definition 5 (Approximate Controllability [39]). System ( 1) is called approximately controllable on [0, τ] if, for every φ ∈ C([−h, 0]; Z), ς 1 ∈ P C(I, Z), and ≥ 0, there exists ṽ ∈ P C(I, U) such that the corresponding solution ς(µ) of (1) satisfies ς(0) = φ(0) and ς(τ) − ς 1 Z ≤ .…”
Section: Lemma 2 ([38]mentioning
confidence: 99%
“…where Ω ⊆ R N is a bounded domain containing the origin, p ∈ (1, ∞), s ∈ (0, 1), 1 < r < q < p, 0 ≤ θ < sp < N, α+β = p * s,θ and λ, µ > 0 are two parameters, p * s,θ = (N−θ)p N−ps is the fractional Hardy-Sobolev exponent, the fractional p-Laplacian operator (−△) s p is the nonlocal operator defined on smooth functions by (−△) s p u(x) = 2 lim are widely studied. We refer the readers to [2,5,6,10,13,[18][19][20][21][22][23][24] and references therein.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional differential equations play a significant role in various fields of science and engineering such as fluid mechanics, mechanics of materials, biology, plasma physics, finance, chemistry, image processing (see, for example, [1][2][3][4]14,[18][19][20]26]). Variable-order fractional calculus is an extension of the constant-order fractional calculus.…”
Section: Introductionmentioning
confidence: 99%