Talk to your doctor or psychiatrist about it. My guess is no. Trileptal is an anti-convulsant, and Abilify is specifically for mental illnesses. They would work differently due to their drug classes and targeted illnesses.
If Abilify is working for you, then you probably shouldn't switch unless it's a price issue that's really making things hard for you. However, if you do switch and it is working for you, you should probably be to something in a similar drug class, which does require you to see whoever is treating your bipolar disorder.
Some anticonvulsants do work for bipolar disorder. I don't know what they specifically treat in bipolar disorder, but if it works similar to antipsychotics in the disorder, it would probably be better to switch to an anticonvulsant rather than continue taking an antipsychotic, provided it works for you. Prolonged usage of antipsychotics can have permanent side effects, but not always.
Trileptal is an anti-convulant that is prescribed as a mood stabilizer but it can be less than effective (although each person responds differently to each medication). Abilify is specifically FDA approved for both mood disorders and psychotic disorders. If a person has a mood disorder that would have any type of psychosis as part of it they would most likely need an antipsychotic. Otherwise there are a wide variety of mood stabilizers although only a psychiatrist would understand the clinical specifics. The most important issue is what are your specific concerns in why you would want it changed and it would be worthwhile to discuss that with your psychiatrist.
This has some worthwhile information on bipolar and mood disorders in general that you could discuss with your psychiatrist:
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