Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ^★-Algebra-Valued Bipolar Metric Spaces

Abstract

In the present paper, we prove common fixed point theorems under different contractive mappings on C★-algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution.

Keywords

• ℂ^★-algebra
• bipolar metric space
• ℂ^★-algebra-valued bipolar metric space
• common fixed point
• fractional differential equation