Solving Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions Using Covariant <i>JS</i>-Contractions

Abstract

This paper investigates the existence, uniqueness, and symmetry of solutions for Φ–Atangana–Baleanu fractional differential equations of order μ∈(1,2] under mixed nonlocal boundary conditions. This is achieved through the use of covariant and contravariant JS-contractions within a generalized framework of a sequential extended bipolar parametric metric space. As a consequence, we obtain the results on covariant and contravariant Ćirić, Chatterjea, Kannan, and Reich contractions as corollaries. Additionally, we substantiate our fixed-point findings with specific examples and derive similar results in the setting of sequential extended fuzzy bipolar metric space.

Keywords

• sequential extended bipolar parametric metric space
• fuzzy fixed-point results
• fractional differential equations
• nonlocal boundary conditions
• <i>JS</i>-contraction