Riemann-Liouville integral, fractional derivative and their applications in probability theory

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.