Boundary Value Problems on the Half-Line with Impulses and Infinite Delay☆☆☆

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Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay (2020, background): “In view of [4, 14], we define the abstract phase space g.”
Results on controllability of Hilfer fractional differential equations with infinite delay via measures of noncompactness (2021, background): “See other properties of MNC (refer to Banas & Goebel [27] and Kamenskii et al. [28]): for all bounded subsets 𝜓 ,𝜓1,𝜓2 of Y, (4) ℛ(𝜓1 +𝜓2) ≤ ℛ(𝜓1) +ℛ(𝜓2), where 𝜓1 +𝜓2 = {x1 + x2 ∶ x1 ∈ 𝜓1, x2 ∈ 𝜓2}; (5) ℛ(𝜓1 ∪ 𝜓2) ≤ max{ℛ(𝜓1),ℛ(𝜓2)}; (6) ℛ(𝜆𝜓) ≤ |𝜆|ℛ(𝜓) for any 𝜆∈R; (7) if Q : E”
Controllability results for impulsive differential systems with finite delay (2012, background): “[13] and Samoilenko and Perestyuk [22] and the papers of [1, 4, 7, 8, 18, 24, 25], where the numerous properties of their solutions are studied and detailed bibliographies are given.”
The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm (2020, background): “Assume x 2 Bv, then for t 2 J, xt 2 Bv (see [62]).”