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Abstract
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In this article, we investigate the existence results of the
solutions for the new types of inclusion problems involving Caputo
and Hadamard fractional derivatives. Utilizing some extended
contractions that are more general than the previous ones which
have been used in the literatures, we deduce some new and
interesting results. In this way, we use
$\alpha-\psi$-contractions and multi-functions. Applying a new
concept of ${\alpha_{s}}^*$-admissibility for Hardy-Rogers-type
$(\hbar, \alpha)-$contractions, we get our findings. Finally, some
examples are given to delineate the efficiency of the theoretical
results.
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