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Recently, Abbas et al. [Enriched multivalued contractions with applications to differential inclusions and dynamic programming, Symmetry 13(8) (2021), 1350] obtained an interesting generalization of the Nadler fixed point theorem by introducing the concept of enriched multivalued contraction in the framework of Banach spaces. In this article, we define a new class of metrics on the family of closed and bounded subsets of a given metric space. Furthermore, fixed point theorems were established for enriched multi-valued contractions by substituting the Hausdorff metric with metrics from a specific class that are either metrically or sequentially equivalent to the Hausdorff metric. Some examples are provided to illustrate the concepts and results presented herein. These results improve, unify, and generalize several comparable results in the literature.

In the present article, we introduce a new type of generalized multivalued orthogonal α-Fcontraction of integral type mappings in the context of orthogonal metric spaces and establish some fixed point results. We construct an example to show the existence of the new type of mappings introduce in this work. Our results substantially unify, generalize and complement the comparable results in the existing literature. As an application of our results, we derive periodic point results for the generalized single valued orthogonal α-F-contraction of integral type mappings in orthogonal metric spaces.

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space ( l q (·) (L p (·)) ). Moreover, it was developed using classical Lebesgue space ( L p ) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not. [ABSTRACT FROM AUTHOR]

In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.

This research endeavour-investigates the enhanced adaptation of the Laplace-based variational iteration method (VIM) tailored specifically for tackling the Duffing Equation. This is accomplished by incorporating the Lagrange multiplier as a strategic tool to effectively address the inherent natural frequency within the Duffing Equation. Using a meticulous comparative analysis, here are juxtapose the analytical outcomes generated by the modified VIM approach with the numerical solution obtained through the application of the renowned Runge-Kutta Fehlberg method (RKF45), implemented by using the powerful mathematical software, MAPLE. Furthermore, by exploring the profound influence of diverse initial conditions on the resulting solution, a diverse array of distinct graphical representations is presented. [ABSTRACT FROM AUTHOR]

Fractional calculus and convex inequalities combine to form a comprehensive mathematical framework for understanding and analyzing a variety of problems. This note develops Hermite-Hadamard, Fej'er, and Pachpatte type integral inequalities within pseudo left-right order relations by applying fractional operators with non-singular kernels. Recently, results have been developed using classical Riemann integral operators in addition to various other partial order relations that have some defects that we explained in literature in order to demonstrate the unique characteristics of pseudo order relations. To verify the developed results, we constructed several interesting examples and provided a number of remarks that demonstrate that this type of fractional operator generalizes several previously published results when different things are set up. This work can lead to improvements in mathematical theory, computational methods, and applications across a wide range of disciplines. [ABSTRACT FROM AUTHOR]

A comprehensive mathematical model is proposed to study two strains of dengue virus with saturated incidence rates and quarantine measures. Imperfect dengue vaccination is also assumed in the model. Existence, uniqueness and stability of the proposed model are proved using the results from fixed point and degree theory. Additionally, well constructed Lyapunov function candidates are also applied to prove the global stability of infection-free equilibria. It is also demonstrated that the model is generalized Ulam-Hyers stable under some appropriate conditions. The model is fitted to the real data of dengue epidemic taken from the city of Espirito Santo in Brazil. For the approximate solution of the model, a non-standard finite difference(NSFD) approach is applied. Sensitivity analysis is also carried out to show the influence of different parameters involved in the model. The behaviour of the NSFD is also assessed under different denominator functions and it is observed that the choice of the denominator function could influence the solution trajectories. Different scenario analysis are also assessed when the reproduction number is below or above one. Furthermore, simulations are also presented to assess the epidemiological impact of dengue vaccination and quarantine measures for infected individuals. [ABSTRACT FROM AUTHOR]

The FitzHugh–Nagumo model has been used empirically to model certain types of neuronal activities. It is also a non-linear dynamical system applicable to chemical kinetics, population dynamics, epidemiology and pattern formation. In the literature, many approaches have been proposed to study its dynamics. In this paper, initially, we have employed cutting-edge tools from discrete dynamics for discretization and fixed points. It has been proven that an exact discrete scheme exists for this paradigm. This project also considers the phase space and integral surfaces of these evolutionary equations. In addition, it carries out a thorough symmetry analysis of this reaction diffusion system to find equivalent systems. Moreover, steady-state solutions are obtained using ansatzes for traveling wave solutions. The existence of infinite traveling wave solutions has also been proven. Yet again, this investigation establishes the potential of symmetry methods to unravel non-linearity. Finally, singular perturbation theory has been employed to obtain analytical approximations and to study stability in different parameter regimes. [ABSTRACT FROM AUTHOR]

Addressing the boundary value problems of fractional-order differential equations hold significant importance due to their applications in various fields. The aim of this paper was to approximate solutions for a class of boundary value problems involving Caputo fractional-order differential equations employing the AA-iterative scheme. Moreover, the stability and data dependence results of the iterative scheme were given for a certain class of mappings. Finally, a numerical experiment was illustrated to support the results presented herein. The results presented in this paper extend and unify some well-known comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new type of two-dimensional convexity by using total-order relations. In the first part of this paper, we examine the Hyers–Ulam stability of two-dimensional convex mappings by using the sandwich theorem. Our next step involves the development of Hermite–Hadamard inequality, including its weighted and product forms, by using a novel type of fractional operator having non-singular kernels. Moreover, we develop several nontrivial examples and remarks to demonstrate the validity of our main results. Finally, we examine approximate convex mappings and have left an open problem regarding the best optimal constants for two-dimensional approximate convexity. [ABSTRACT FROM AUTHOR]

A patient co-infected with COVID-19 and viral hepatitis B can be at more risk of severe complications than the one infected with a single infection. This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19. The model is fitted to real COVID-19 data from Pakistan. The proposed model incorporates logistic growth and saturated incidence functions. Rigorous analyses using the tools of stochastic calculus, are performed to study appropriate conditions for the existence of unique global solutions, stationary distribution in the sense of ergodicity and disease extinction. The stochastic threshold estimated from the data fitting is given by: ℛS0 = 3.0651. Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases. The effects of stochastic white noise intensities are also highlighted. [ABSTRACT FROM AUTHOR]

Mathematical inequalities supporting interval-valued stochastic processes are rarely addressed. Recently, Afzal et al. introduced the notion of h-Godunova-Levin stochastic processes and developed Hermite-Hadamard and Jensen type inequalities in the setting of interval-valued functions. This note introduces a more generalized class of Godunova-Levin stochastic process that unifies several previously published results through the use of Kulisch-Miranker type order relations that are rarely discussed in relation to stochastic processes. Further, it is the first time that fractional version of Hermite-Hadamard inequality has been developed by using interval-valued stochastic processes in conjunction with a classical operator. Moreover, we give new modified forms for Ostrowski type results and present a new way to treat Jensen type inclusions under interval stochastic processes by using a discrete sequential form. We end with an open problem regarding Milne type results and discuss the importance of different types of order relations related to inequality terms in interval-valued settings. [ABSTRACT FROM AUTHOR]

This note introduces a new class of preinvexity called (h 1 , h 2) -Godunova-Levin preinvex functions that generalize earlier findings. Based on these notions, we developed Hermite-Hadamard, weighted Fejér, and trapezium type inequalities. Furthermore, we constructed some non-trivial examples in order to verify all the developed results. In addition, we discussed some applications related to the trapezoidal formula, probability density functions, special functions and special means. Lastly, we discussed the importance of order relations and left two open problems for future research. As an additional benefit, we believe that the present work can provide a strong catalyst for enhancing similar existing literature. [ABSTRACT FROM AUTHOR]