Fixed-point theorems of F ⋆ − ( ψ , ϕ ) ${F}^{\star}- ( \psi,\phi )$ integral-type contractive conditions on 1 E $1_{E}$ -complete multiplicative partial cone metric spaces over Banach algebras and applications

Abstract

Abstract In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach contraction principle by constructing a special type of contractive restrictions of integral forms for weak contraction mappings defined on 1 E $1_{E}$ -complete multiplicative partial cone metric spaces over Banach algebras and formulate some existence and uniqueness results regarding the fixed-point theorems using some integrative conditions. Moreover, we validate the significance our results and exploit them to find the unique solution of a fractional nonlinear differential equation of Caputo type, which complements some previously well-known generalizations found in the literature.

Keywords

• Multiplicative algebra cones
• Multiplicative segments
• Multiplicative partial cone metric spaces over Banach algebras
• Integral-type inequalities
• Fixed points