Abstract:

The authors discussed the differential equation involving the distributional derivative x′=f(x,t) using the properties and methods
 of generalized ordinary differential equations. Then used the results of the generalized ordinary differential equations to prove the existence and uniqueness theorem of solutions to differential equation involving the distributional derivative.

Key words: generalized ordinary differential equation, HenstockKurzweil integral, D-HK integral, existence, uniqueness, distributional derivative