Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for $\alpha$-Admissible $F\left({\psi }_{}\right)$

Abstract

In this paper, we investigate the existence of a unique coupled fixed point for α−admissible mapping which is of Fψ1,ψ2−contraction in the context of M−metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

“…There are many other important aspects and applications of proximity point theory as well as fixed point theory in different directions [18,19]. In 2020, Karapinar et al [20] discussed the sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations. The application of our established results for solving fractional hybrid differential equations as well as nonlinear matrix equations provides scope for future discussion.…”

S ∗ p ‐ b -Partial Metric Spaces with some Results in Common Fixed Point Theo

“…Since w 2n and w 2n+1 are comparable, then we may assume that S * P b ðw 2n , w 2n , w 2n+1 Þ > 0, for every n ∈ N. If not, then w 2n = w 2n+1 for some n. For all those n, using (24), we obtain…”

“…Remark 36. It will be interesting to find more applications to our current paper in other fields, see [11,[19][20][21][22][23][24][25][26][27][28][29].…”