Solution of a nonlinear fractional-order initial value problem via a C ∗ $\mathscr{C}^{*}$ -algebra-valued R $\mathcal{R}$ -metric space

Abstract

Abstract In this article, we prove new common fixed-point theorems on a C ∗ $\mathscr{C}^{*}$ -algebra-valued R $\mathcal{R}$ -metric space. An example is given based on our obtained results. To enhance our results, a strong application based on the fractional-order initial value problem is provided.

Keywords

• Common fixed point
• R $\mathcal{R}$ -metric space
• C ∗ $\mathscr{C}^{*}$ -algebra
• C ∗ $\mathscr{C}^{*}$ -algebra-valued R $\mathcal{R}$ -metric space