Existence of nontrivial solutions to fractional Kirchhoff double phase problems

In this present paper, we concern the discussion of multiplicity non-trivial solution for a new class of fractional differential equations of the Kirchhoff type in the \(\psi \) $\psi$ -fractional space \(\mathbb {S}^{\alpha ,\beta ;\psi }_{\mathcal {H},0}(\Lambda )\) ${\mathbb{S}}_{\mathcal{H},0}^{\alpha ,\beta ;\psi }(\mathrm{\Lambda })$ via critical point result and variational methods.