Existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions

By Khalil Ezzinbi, Xianlong Fu, Khalid Hilal. 2004

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Mild solutions for semilinear fractional differential equations. (2009, background): “This allows us to define the fractional power A for 0 < α < 1, as a closed linear operator on its domain D(A) with inverse A−α(see [8]).”
Monotone Iterative Technique for a Class of Semilinear Evolution Equations with Nonlocal Conditions (2013, background): “The importance of nonlocal conditions have been discussed in [2,4–6, 8–15].”
Existence of mild solutions for fractional evolution equations with mixed monotone nonlocal conditions (2013, background): “Since it is demonstrated that the nonlocal problems have better effects in applications than the traditional Cauchy problems, differential equations with nonlocal conditions were studied by many authors and some basic results on nonlocal problems have been obtained, see [16–30], and the references t”
Existence of Solutions for Impulsive Neutral Integro-Differential Inclusions with Nonlocal Initial Conditions via Fractional Operators (2009, background): “Moreover, F : J × X 1 2 → X 1 2 , A 1 2 F : J × X 1 2 → X 1 2 and G : J × X 1 2 → X (see [12]).”