his study proposes Maia ${\alpha}^*-\psi$ contractive type multi-valued mappings and states some new interesting results. Introducing some concepts as sub-guided, $T$-chained and ${\alpha}^*$-admissibility we prove new results in partially ordered metric spaces, which improve and develop different known results on the literature. As utilizations, we investigate the existence and uniqueness of solutions of Hadamard-type fractional inclusions. In comparison to other existing methods, our theorems are capable of studying the existence and uniqueness of solutions of inclusions without using selection property.
