In this paper, we investigated the problem of describing the form of higher Jordan triple derivations on trivial extension algebras. We show that every higher Jordan triple derivation on a $2$-torsion free *-type trivial extension algebra is a sum of a higher derivation and a higher anti-derivation. As for its applications, higher Jordan triple derivations on triangular algebras are characterized.

The aim of the paper was to give a description of nonlinear Jordan triple derivable mappings on trivial extension algebras. We proved that every nonlinear Jordan triple derivable mapping on a $2$-torsion free $\ast$-type trivial extension algebra is a sum of an additive derivation and an additive antiderivation. As an application, nonlinear Jordan triple derivable mappings on triangular algebras were characterized.