Existence of solutions to fractional order ordinary and delay differential equations and applications.

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Positive solutions of fractional differential equations with derivative terms (2012, unknown): “…the time when Leibnitz and Newton invented differential calculus and the tools of fractional calculus have been available and applicable to various fields of study, the qualitative and quantitative investigation of the theory of fractional differential equations has been started recently [1, 2, 3].”
Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative (2013, background): “The literature is very rich in works on well-posedness for fractional differential equations [8–17] (see also the books [1, 2, 4, 5] and the survey paper [18]) to cite but a few.”