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Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives

Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54, 10-710 Olsztyn, Poland
Symmetry 2019, 11(11), 1366; https://doi.org/10.3390/sym11111366
Received: 21 September 2019 / Revised: 18 October 2019 / Accepted: 23 October 2019 / Published: 4 November 2019
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Application)
This paper deals with the initial value problem for linear systems of fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives. Some basic properties of fractional derivatives and antiderivatives, including their non-symmetry w.r.t. each other, are discussed. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by examples. View Full-Text
Keywords: fractional differential equation; Riemann–Liouville derivative; Caputo derivative; state transition matrix; generalized Peano–Baker series fractional differential equation; Riemann–Liouville derivative; Caputo derivative; state transition matrix; generalized Peano–Baker series
MDPI and ACS Style

Matychyn, I. Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann–Liouville and Caputo Derivatives. Symmetry 2019, 11, 1366.

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