The purpose of this paper, is studying the existence and nonexistence of positive solutions to a class of a following tripled system of fractional dierential equations.whereand D is the standard Riemann-Liouville fractional derivative. Also, we provide some examples to demonstrate the validity of our results.

In this manuscript, we investigate the existence and uniqueness of a common fixed point for the self-mappings defined on quasi-cone metric space over a divisible Banach algebra via an auxiliary mapping ϕ.

Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of ϕ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by usingϕ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions andfollowing their work with introducing two mappings $\mathcal{T}$ and $\mathcal{S}$ we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.

Best proximity point theorems for self-mappings and multi-functions were investigated with different conditions on spaces and the contractions of mappings. In this paper, we will prove best proximity point theorems for some generalized multi-functions that we call [Formula: see text]-proximal multi-functions, which are of two types, [Formula: see text]-proximal multi-functions of the first and second kind.