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Solving fractional-order ordinary differential equations via Adomian decomposition method
Šustková, Apolena ; Řehák, Pavel (referee) ; Nechvátal, Luděk (advisor)
This master's thesis deals with solving fractional-order ordinary differential equations by the Adomian decomposition method. A part of the work is therefore devoted to the theory of equations containing differential operators of non-integer order, especially the Caputo operator. The next part is devoted to the Adomian decomposition method itself, its properties and implementation in the case of Chen system. The work also deals with bifurcation analysis of this system, both for integer and non-integer case. One of the objectives is to clarify the discrepancy in the literature concerning the fractional-order Chen system, where experiments based on the use of the Adomian decomposition method give different results for certain input parameters compared with numerical methods. The clarification of this discrepancy is based on recent theoretical knowledge in the field of fractional-order differential equations and their systems. The conclusions are supported by numerical experiments, own code implementing the Adomian decomposition method on the Chen system was used.
Analysis of fractional-order two-dimensional models
Šustková, Apolena ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
This bachelor's thesis deals with the analysis of fractional-order two-dimensional models. The analysis itself is preceded by the introduction to the basic issues concerning the integer-order and fractional-order theory. Investigations are carried out for two specific models, Lotka-Volterra model and the Brusselator, the focus is put primarily on stability of the equilibrium points. The results are supported by appropriate phase portraits that were, for the non-integer case, created using the code for numerical solution of fractional differential equations.

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1 Šůstková, Anna
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