This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields of applied sciences. In the present article, a class of q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for a numerical solution of a distinct class of fractional differential inclusions have been achieved with the help of Schaefer type and Banach contraction fixed point theorems. A physical example is also provided to validate the hypothesis of the main results. The notion of q-rung orthopair fuzzy mappings along with the use of fixed point techniques and a new-fangled Caputo type fractional derivative are the principal novelty of this article.

Hybrid contractions serve as a flexible and versatile framework for establishing fixed-point Theorems and analyzing the convergence of iterative algorithms. This paper demonstrates the adapted form of the admissible hybrid fuzzy $\mathfrak{Z}$-contraction in the perspective of £-fuzzy set-valued maps for extended ♭-metric spaces. Sufficient criteria for obtaining £-fuzzy fixed points for this contraction have been established. In addition, the hypotheses of its main result are endorsed by some nontrivial supportive examples featuring graphical illustrations. Consequently, the concept of graphical extended ♭-metric spaces is introduced and a £-fuzzy fixed point result in the context of newly defined space is derived. Illustrative examples, incorporating relevant graphs, are provided with the support of a computer simulation to validate the established results, enhancing the understanding of the underlying notions and investigations. The concepts presented here not only considerably improve, enrich, and extend a number of well-known pre-existing fixed-point results but also assemble and merge several ones in the corresponding domain.

The primary objective of perturbed metric spaces was to set route for the advancement of problems involving fixed point findings for a distraught structure, where errors inevitably affected the measurement of distance between two points. This objective developed into a broadly applicable context when the range set of the distance function was a $ C^{*} $-algebra. Inspired by this, the notion of $ C^{*} $-algebra-valued perturbed modular metric space was introduced in this paper. Thereafter, some fixed point theorems in the new space were studied, using paired contractive mappings. In order to demonstrate the novelty of the concepts presented herein and to generalize some significant related discoveries in the literature, contrasting examples were given. Under this comparative illustration, numerical and graphical approaches were adopted to study the rate of convergence of Picard-type and paired contractive operators. As an application, new conditions for the existence and uniqueness of a solution to fourth-order boundary value problems were obtained.

In this manuscript, the concept of $ \digamma $-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of $ G $-metric space, which is termed Jaggi-Suzuki-type hybrid $ \digamma $-($ G $-$ \alpha $-$ \phi $)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein.

A novel and generalized class of fractional differential inclusions has been investigated under a combination of nonlocal, non-separated, multipoint, and integral boundary conditions. Fractional derivatives have been employed to capture memory effects and enhance the modeling accuracy of real-world phenomena. Uncertainty has been addressed through the formulation of set-valued differential inclusions. The proposed boundary conditions have been designed to encompass a wide spectrum of both local and nonlocal types previously reported in the literature. The existence of solutions has been established via the Bohnenblust–Karlin fixed-point theorem. The applicability and effectiveness of the main results have been demonstrated through concrete examples.