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The main intention of this article is that new techniques of existence theory are used to derive some required criteria pertinent to a given fractional multi-term problem and its inclusion version. In such an approach, we do our research on a fractional integral equation corresponding to the mentioned BVPs. In more precise words, by virtue of this integral equation, we construct new operators which belong to a special category of functions named α -admissible and α - ψ -contraction maps coupled with operators having (AEP)-property. Next, by considering some new properties on the existing Banach space having properties (B) and ( C α ) $(C_{\alpha })$ , our argument for ensuring the existence of solutions is completed. In addition, we also add two simulative examples to review our findings by a numerical view.

On solutions of fractional multi-term sequential problems via some special categories of functions and (AEP)-property