Theorems on Some Families of Fractional Differential Equations and Their Applications - (:unkn) unknown (ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS, 2019)
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration equation with fractional damping and the Bagley-Torvik equation.
Keywords: fractional calculus; fractional differential equation; Caputo derivative; Laplace transform