Solution of linear fractional differential equations with constant coefficients. (English) Zbl 0918.34010

Podlubny, I.

Rusev, P. (ed.) et al., Transform methods and special functions. Proceedings of the 1st international workshop, Bankya, Bulgaria, August 12–17, 1994. Sofia: SCT Publishing, 227-237 (1995).

Summary: A method for obtaining explicit analytical solutions to linear differential equations of arbitrary real order with constant coefficients, and initial value problems for such equations, are presented and illustrated by examples.
For the entire collection see [Zbl 0914.00064].

MSC:

34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
26A33	Fractional derivatives and integrals
33E20	Other functions defined by series and integrals
33E30	Other functions coming from differential, difference and integral equations
44A10	Laplace transform
44A20	Integral transforms of special functions
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
34A30	Linear ordinary differential equations and systems
34A05	Explicit solutions, first integrals of ordinary differential equations

Keywords:

explicit analytical solutions; initial value problems