My hunch is that your appliances have nothing to do with this. Rather, you have bad wires.
GFCI is not the same as AFCI. They serve very different functions and operate quite differently.
GFCI is for life safety and is conceptually incredibly simple - check to see if hot and neutral have the same current. That's it. Self-testing, indicator lights, etc. are all icing on the cake. But the core is: Compare the current. That can be done with very basic components, which is why it has been available for decades, with gradual increase in required locations as the cost has gone down.
AFCI is for fire safety. It is conceptually, and practically, quite complex. You don't need a microprocessor to figure out GFCI. You can - and modern GFCI (whether breaker or receptacle) uses a microprocessor for self-test and other features, but you don't need it. But AFCI is a much more complex thing, that pretty much requires a microprocessor to analyze the power flow to determine if it is doing "bad things" that would indicate a likely arcing situation that could lead to a fire.
As a result, GFCI is required primarily in wet places - kitchen, bathroom, laundry, outdoors, though recently expanded to include other areas. AFCI, on the other hand, started in the other areas - bedrooms, then living rooms, etc.
There is some overlap now, and it will likely increase over time, depending on NEC version. So you may be required to include AFCI for new circuits in your kitchen. If these are existing circuits, I would recommend installing GFCI (either receptacle or breaker) if you do not already have it (the life safety advantage in a kitchen has been obvious for decades) but not to install AFCI unless required by your jurisdiction.