An exploration of combined dynamic derivatives on time scales and their applications

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Notes on the diamond-α dynamic derivative on time scales (2007, background): “including the standard and ∇ derivatives, in approximating functions and solutions of nonlinear differential equations has been explored [3,4,6,10].”
On the diamond-alpha riemann integral and mean value theorems on time scales (2008, methodology): “Keywords: time scales, diamond-alpha integral, Fermat’s theorem for stationary points, mean value theorems.”
Diamond- Jensen's Inequality on Time Scales (2007, methodology): “Equality (1) is the definition of fα(t) found in [18].”