Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions

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Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay (2020, background): “Several researchers done enormous works inspired by these articles; one can refer to [5, 9, 10, 27, 41, 53, 54].”
Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal conditions (2013, background): “Recently, Wang and Yang [16]; Wang, Xiao, and Liang [17]; Li, Liang, and Xu [18]; Zhou and Jiao [19]; Wang et al.”
Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators (2017, background): “1) have been obtained, for instance in [4, 9, 11, 13, 14, 19, 24, 27] and the references therein.”
Controllability of Sobolev type fractional evolution systems (2014, methodology): “Here, we mixed and modify the conditions and techniques used in [26, 32, 34, 35] to prove the controllability results.”