scholarly journals Solution of linear fractional order systems with variable coefficients

2020 ◽  
Vol 23 (3) ◽  
pp. 753-763
Author(s):  
Ivan Matychyn ◽  
Viktoriia Onyshchenko
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Initial Value Problem ◽  
Transition Matrix ◽  
State Transition ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Fractional Order Systems ◽  
Initial Value ◽  
Theoretical Results

AbstractThe paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann–Liouville derivatives. 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 an example.

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

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1366 ◽  
Author(s):  
Ivan Matychyn
Keyword(s):  
Transition Matrix ◽  
Fractional Derivatives ◽  
State Transition ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Initial Value ◽  
Fractional Systems ◽  
Caputo Derivatives ◽  
Fractional Differential ◽  
Theoretical Results

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.

The numerical algorithms for discrete Mittag-Leffler functions approximation

2019 ◽  
Vol 22 (1) ◽  
pp. 95-112 ◽  
Author(s):  
Ang Li ◽  
Yiheng Wei ◽  
Zongyang Li ◽  
Yong Wang
Keyword(s):  
Transition Matrix ◽  
State Transition ◽  
Numerical Algorithms ◽  
The State ◽  
State Transition Matrix ◽  
Numerical Implementation ◽  
Science And Engineering ◽  
Implementation Method ◽  
Theoretical Results

Abstract Motivated essentially by the success of the applications of the discrete Mittag-Leffler functions (DMLF) in many areas of science and engineering, the authors present, in a unified manner, a detailed numerical implementation method of the Mittag-Leffler function. With the proposed method, the overflow problem can be well solved. To further improve the practicability, the state transition matrix described by discrete Mittag-Leffler functions are investigated. Some illustrative examples are provided to verify the effectiveness of the proposed theoretical results.

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