ON SOME NON-INSTANTANEOUS IMPULSIVE DIFFERENTIAL EQUATIONS WITH FRACTIONAL BROWNIAN MOTION AND POISSON JUMPS

By using Monch fixed point theorem, fractional calculus and stochastic analysis, sufficient conditions for existence solutions of non-instantaneous impulsive Hilfer-Katugampola fractional differential equations of order 1/2 < alpha < 1 and parameter 0 <= beta <= 1 with fractional Brownian motion (fBm), Poisson jumps, and with nonlocal conditions are established. Finally, an example is given to illustrate the results obtained.

Automated summary

By using Monch fixed point theorem, fractional calculus, and stochastic analysis, this paper establishes sufficient conditions for the existence of solutions to non-instantaneous impulsive Hilfer-Katugampola fractional differential equations of order 1/2 < alpha < 1 and parameter 0 <= beta <= 1 with fractional Brownian motion (fBm), Poisson jumps, and nonlocal conditions. An example is provided to illustrate the obtained results.