  In this paper, we will consider a class of locally $\Phi$-Beilinson-Green
algebras, where $\Phi$ is an infinite admissible set of the integers, and show
that symmetric approximation sequences in $n$-exangulated categories give rise
to derived equivalences between quotient algebras of locally
$\Phi$-Beilinson-Green algebras in the principal diagonals modulo some
factorizable ghost and coghost ideals by the locally finite tilting family.
Then we get a class of derived equivalent algebras that have not been obtained
by using previous techniques. From higher exact sequences, we obtain derived
equivalences between subalgebras of endomorphism algebras by constructing
tilting complexes, which generalizes Chen and Xi's result for exact sequences.
From a given derived equivalence, we get derived equivalences between locally
$\Phi$-Beilinson-Green algebras of semi-Gorenstein modules. Finally, from given
graded derived equivalences of group graded algebras, we get derived
equivalences between associated Beilinson-Green algebras of group graded
algebras.
