Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives

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On Delta and Nabla Caputo Fractional Differences and Dual Identities (2011, background): “For details in the continuous counterparts see [26].”
Generalized fractional derivatives and Laplace transform (2020, background): “Let the function f(t) ∈ Cg[a, T ] and of g(t)- exponential order such that f ([1])(t) is piecewise continuous over every finite interval [a, T ].”
Results on controllability of non-densely characterized neutral fractional delay differential system (2021, background): “Due to the colossal opportunity and usage, considerable papers have been concerned to articulate the solutions of fractional systems [1, 2, 4, 6, 7, 9, 10, 11, 13, 15, 17, 19, 20, 24, 26, 28, 29, 33, 35, 36] and the”
On fractional derivatives with exponential kernel and their discrete versions (2016, methodology): “For equations in the classical fractional case with composition of left and right fractional derivatives with the action of the Q−operator we refer to [27].”
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel (2016, background): “For such a composition in the classical fractional case together with the action of the Q−operator we refer to [15].”