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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Riemann-Liouville integral, fractional derivative and their applications in probability theory
 Kršek, Daniel ; Maslowski, Bohdan (advisor) ; Čoupek, Petr (referee)
Fractional integrals and derivatives in a sense generalize common integrals and derivatives. They can be used to define the integral b a f(x) dg(x) on a bounded interval for large set of integrands f and integrators g, in ge- neral, of unbounded variation. This concept may be utilized in theory of stochastic differential equations, where the standard random processes are not of bounded variation, yet they admit a version with Hölder continuous sample paths. This thesis deals with a particular type of multidimensional differential equations, where subject to certain conditions an existence of a unique solution may be proved. It presents the proof of continuous depen- dence of solutions on initial condition. Furthermore, this thesis analyzes the situation in which coefficients in equations continuously depend on a para- meter from certain metric space. For such a situation, the thesis introduces a proof of continuous dependence of solutions on these parameters. 1
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New Methodology Of Parkinsonic Dysgraphia Analysis By Online Handwriting Using Fractional Derivatives
 Mucha, Ján
Parkinson’s disease (PD) is the second most frequent neurodegenerative disorder. One typical hallmark of PD is disruption in execution of practised skills such as handwriting. This paper introduces a new methodology of kinematic features calculation based on fractional derivatives applied on PD handwriting. Discrimination power of basic kinematic features (velocity, acceleration, jerk) was evaluated by classification analysis (using support vector machines and random forests). For this purpose, 37 PD patients and 38 healthy controls were enrolled. In comparison to results reported in other works, we proved that FDE in online handwriting analysis brings promising improvements. The best result of multivariate analysis was achieved with 83:89% classification accuracy in combination with 5 features using only one handwriting task (overlapped circles). This study reveals an impact of fractional derivatives based features in analysis of Parkinsonic dysgraphia.
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