Singular regularization of operator equations in L1 spaces via fractional differential equations
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An abstract causal operator equation y=Ay defined on a space of the form L1([0,τ],X), with X a Banach space, is regularized by the fractional differential equation ε(Dα0yε)(t) = -yε(t) + (Ayε)(t), t ∈ [0,τ], where Dα0 denotes the (left) Riemann-Liouville derivative of order α ∈ (0,1). The main procedure lies on properties of the Mittag-Leffler function combined with some facts from convolution theory. Our results complete relative ones that have appeared in the literature; see, e.g.  in which regularization via ordinary differential equations is used.
CitationKarakostas, G. L., & Purnaras, I. K. (2016). Singular regularization of operator equations in L1 spaces via fractional differential equations. Electronic Journal of Differential Equations, 2016(01), pp. 1-15.
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