Theorems on some families of fractional differential equations and their applications. (English) Zbl 07144728

The paper is concerned with solving some fractional differential equations of Riemann-Liouville and Caputo types using Laplace transform methods. The authors begin by providing some background to exact and numerical solution of fractional differential equations. They go on to consider several different families of fractional differential equation and they give results that show how the Laplace transform approach provides an exact formula for the solution. The paper ends with some worked examples that apply their method.


26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
44A10 Laplace transform
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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