ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS AND SOME TIME DISCRETIZATIONS

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Fractional differential equations: a novel study of local and global solutions in Banach spaces (2013, unknown): “(See, for instance, [11, 21, 62, 66]).”
Approximate Controllability of Fractional Differential Equations with State-Dependent Delay (2012, unknown): “[29] A closed and densely defined operator A is said to be sectorial if there exist 0 < θ < π/2, M̂ > 0 and μ ∈ R such that its resolvent exists outside the sector μ+ Sθ := {μ+ λ : λ ∈ C, |arg(−λ)| < θ}, and ‖(λ−A)−1‖ ≤ M̂ |λ− μ| , λ / ∈ μ+ Sθ.”
Mild solutions for abstract fractional differential equations (2013, background): “Note that the existence of S (t) satisfying this condition follows, for example, if A generates a cosine function or if we assume that A is ! sectorial with angle 0 < (1 /2), see [36].”
Almost automorphic mild solutions to fractional differential equations (2008, background): “1) is equivalent to solve an integral equation of convolution type (see [3], [5]).”
Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions (2014, unknown): “For more details see [1] [2] [3] [4] [5] [10] [11] [14] [21].”