Fractional Kirchhoff-type systems via sub-supersolutions method in ${\mathbb{H}}_p^{\alpha ,\beta ;\psi }(\mathrm{\Omega })$

In the present paper, we first establish a version of the abstract lower and upper-solution method for our class of operators. In this sense, we investigated the main objective of this paper, that is, the existence of a positive solution for a new class of fractional systems of the Kirchhoff type with $\psi$-Hilfer operators via the method of sub and supersolutions in $\psi$-fractional space ${\mathbb{H}}_p^{\alpha ,\beta ;\psi }(\mathrm{\Omega })$