Differential equations of fractional order:methods results and problem —I

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Algorithms for the fractional calculus: A selection of numerical methods (2005, background): “For the case of Caputo FDEs, these additional conditions are just the static initial conditions listed in (14), which are akin to those of classical ODEs, and are therefore familiar to us. In contrast, for Riemann–Liouville FDEs, these additional conditions constitute certain fractional derivatives ”
Existence of Solutions for Fractional Differential Equations with Multi-point Boundary Conditions at Resonance on a Half-line (2011, background): “Apart from diverse areas of mathematics, fractional differential equations arise in a variety of different areas such as rheology, fluid flows, electrical networks, viscoelasticity, chemical physics, and many other branches of science (see [1, 9, 10, 11, 16, 17, 25] and references cited therein).”
Positive solutions for boundary value problem of nonlinear fractional differential equation (2005, neutral): “For details, see [4, 6, 7, 8] and the references therein.”
FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION (2008, neutral): “For details, see [4, 6, 7, 8] and the references therein.”