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The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S -metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, quasi-contractions, Ćirić–Reich–Rus-type contractions, Hardy–Rogers-type contractions, Reich-type contractions, interpolative Kannan contractions, interpolative Chatterjee contractions, among others, with their generalizations in S -metric spaces. We offer significant examples to substantiate the reliability of our results. This study also establishes consequential fixed-point results and applies them to nonlinear fractional differential equations and the boundary value problem for homogeneous transverse bars. At the end of the manuscript, we present an important open problem. [ABSTRACT FROM AUTHOR]

In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is − Δ p u = β | ∇ u | q + c | u | p − 2 u + f in   Ω , u = 0 on   ∂ Ω , where Ω is an open bounded subset of R N , N ≥ 2 , 1 < p < N , Δ p u is the so-called p-Laplace operator, and p − 1 < q < p . We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

The purpose of this research is to examine the uniqueness and existence of the (ω , ρ) -BVP solution for a particular solution to a class of Hadamard fractional differential equations with impulsive boundary value requirements on Banach spaces. The notion of Banach contraction and Schaefer's theorem are used to prove the study's key findings. In addition, we offer the prerequisites for the set of solutions to the investigated boundary value with impulsive fractional differential issue to be convex. To enhance the comprehension and practical application of our findings, we offer two illustrative examples at the end of the paper to show how the results can be applied. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the Caputo fractional differential equation involving the ρ (τ) Laplacian operator and nonlocal multi-point of Riemann–Liouville's fractional integral. We also prove the uniqueness of the positive solutions for Boyd and Wong's nonlinear contraction via the Guo–Krasnoselskii fixed-point theorem in Banach spaces. Finally, we illustrate the theoretical results and show that by solving the nonlocal problems, it is possible to obtain accurate approximations of the solutions. An example is also provided to illustrate the applications of our theorem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce new forms of quasi-contractions in metric-like spaces and initiate more general conditions for the existence of invariant points for such operators. The proposed notions are then applied to study novel existence criteria for the existence of solutions to two-point boundary value problems in the domains of integer and fractional orders. To attract further research in this direction, important consequences are deduced and discussed to indicate the novelty and generality of our proposed concepts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new class of boundary value problems, consisting of a mixed-type ψ 1 -Hilfer and ψ 2 -Caputo fractional order differential equation supplemented with integro-differential nonlocal boundary conditions. The uniqueness of solutions is achieved via the Banach contraction principle, while the existence of results is established by using the Leray–Schauder nonlinear alternative. Numerical examples are constructed illustrating the obtained results. [ABSTRACT FROM AUTHOR]

In the present work, we have introduced a new type of (ξ , ω) -weakly cyclic generalized contraction in the setting of metric spaces and established some fixed-point results. Fixed-point results are useful in establishing the existence of unique solution to differential equations. We have supplemented the derived results with suitable non-trivial examples with an application to the Boundary Value Problem, generalizing some known results. The analytical result has been verified with numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper we investigate the criteria for the existence of solutions for single-valued as well as multi-valued boundary value problems involving (k , ψ) -Hilfer fractional derivative operator of order in (1 , 2 ] , equipped with nonlocal integral multi-point boundary conditions. For the single-valued case, we rely on fixed point theorems due to Banach and Krasnosel'skiĭ, and Leray–Schauder alternative to establish the desired results. The existence results for the multi-valued problem are obtained by applying the Leray–Schauder nonlinear alternative for multi-valued maps for convex-valued case, while the nonconvex-valued case is studied with the aid of Covit–Nadler's fixed point theorem for multi-valued contractions. Numerical examples are presented for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]

Considering the ω -distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using ω -distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation. [ABSTRACT FROM AUTHOR]

A novel fixed-point theorem based on the degree of nondensifiability (DND) is used in this article to examine the existence of solutions to a boundary value problem containing the ψ -Caputo fractional derivative in Banach spaces. Besides that, an example is included to verify our main results. Moreover, the outcomes obtained in this research paper ameliorate and expand some previous findings in this area. [ABSTRACT FROM AUTHOR]

The main intention of the present research study is focused on the analysis of a Caputo fractional integro-differential boundary problem (CFBVP) in which the right-hand side of supposed differential equation is represented as a sum of two nonlinear terms. Under the integro-derivative boundary conditions, we extract an equivalent integral equation and then define new operators based on it. With the help of three distinct fixed-point theorems attributed to Krasnosel'skiĭ, Leray–Schauder, and Banach, we investigate desired uniqueness and existence results. Additionally, the dependence criterion of solutions for this CFBVP is checked via the generalized version of the Gronwall inequality. Next, three simulative examples are designed to examine our findings based on the procedures applied in the theorems. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new nonlocal boundary value problem of integro-differential equations involving mixed left and right Caputo and Riemann–Liouville fractional derivatives and Riemann–Liouville fractional integrals of different orders. Our results rely on the standard tools of functional analysis. Examples are constructed to demonstrate the application of the derived results. [ABSTRACT FROM AUTHOR]

We consider the periodic boundary value problem (PBVP) for a semilinear fractional-order delayed functional differential inclusion in a Banach space. We introduce and study a multivalued integral operator whose fixed points coincide with mild solutions of our problem. On that base, we prove the main existence result (Theorem 4). We present an example dealing with existence of a trajectory for a time-fractional diffusion type feedback control system with a delay satisfying periodic boundary value condition. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for a new class of fractional q-integro-difference equations involving Riemann-Liouville q-derivatives and a q-integral of different orders, supplemented with boundary conditions containing q-integrals of different orders. The first existence result is obtained by means of Krasnoselskii's fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the contractive type inequalities for the iteration of the mapping at a given point in the setting of dislocated metric space. We consider an example to illustrate the validity of the given result. Further, as an application, we propose a solution for a boundary value problem of the second order differential equation. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new extension of b-metric spaces, called controlled metric type spaces, by employing a control function α (x , y) of the right-hand side of the b-triangle inequality. Namely, the triangle inequality in the new defined extension will have the form, d (x , y) ≤ α (x , z) d (x , z) + α (z , y) d (z , y) , for   all x , y , z ∈ X. Examples of controlled metric type spaces that are not extended b-metric spaces in the sense of Kamran et al. are given to show that our extension is different. A Banach contraction principle on controlled metric type spaces and an example are given to illustrate the usefulness of the structure of the new extension. [ABSTRACT FROM AUTHOR]