We consider the numerical solution of one type integro-differential equation by a probability method based on fundamental martingale mixed Gaussian processes. As an application, we try to simulate estimation ruin with an unknown parameter driven not classical Levy process, but fractional Brownian motion.

This paper is devoted to the study of stochastic fractional differential equations. Particularly, we existence and uniqueness solutions nonlinear weighted impulsive ψ -Hilfer neutral integro-fractional system with infinite delay. We obtain results help fixed-point theorems Banach contraction principle. Additionally, inve...

The paper presents the foundations of theory linear fractional Volterra integro-differential equations convolution type in Banach spaces. It is established that existence a resolvent operator for such equivalent to well-posedness formulation initial problem them. Within framework this approach, theorem Hille–Yosida proved.