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Ordered Bipolar Metric Spaces and Fixed-Point Results With an Application to Solution of Fractional Differential Equations

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  • Deepika Adhikari
  • Naveen Chandra
  • Mohammad Sajid

Abstract

The aim of this paper is to introduce the concept of an ordered bipolar metric space in which we establish some fixed-point theorems for contravariant mappings under a generalized nonlinear rational-type contractive condition. Moreover, we analyze the monotonicity of the second iteration of the mapping, which is inherently covariant. We also adapt the celebrated techniques of Ran and Reurings in the settings of contravariant mappings, which have not been studied previously. In addition, we give an application to the existence of a unique solution to nonlinear fractional differential equations, and the obtained results are supported by illustrative examples.

Suggested Citation

  • Deepika Adhikari & Naveen Chandra & Mohammad Sajid, 2026. "Ordered Bipolar Metric Spaces and Fixed-Point Results With an Application to Solution of Fractional Differential Equations," Journal of Mathematics, Hindawi, vol. 2026, pages 1-14, June.
    • Handle: RePEc:hin:jjmath:4663643
    DOI: 10.1155/jom/4663643
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