Geodesic
Theorems on some families of fractional differential equations and their applications
Applications of Mathematics, Tome 64 (2019) no. 5, pp. 557-579 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2019.0031-19
Classification : 26A33, 34A08, 44A10, 44A15
Keywords: fractional calculus; fractional differential equation; Caputo derivative; Laplace transform 
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     title = {Theorems on some families of fractional differential equations and their applications},
     journal = {Applications of Mathematics},
     pages = {557--579},
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Bozkurt, Gülçin; Albayrak, Durmuş; Dernek, Neşe. Theorems on some families of fractional differential equations and their applications. Applications of Mathematics, Tome 64 (2019) no. 5, pp. 557-579. doi: 10.21136/AM.2019.0031-19

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