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This article discusses changes in heat transfer resulting from laser pulses and magnetic fields produced in thermoelastic materials under initial stress. This paper introduces a novel approach to modeling generalized thermoelastic materials by including fractional time derivatives with Eringen's non‐local thermoelastic theory. This model incorporates both the Caputo–Fabrizio and the Atangana–Baleanu derivatives, which are novel forms of fractional derivatives in the domain of fractional calculus. Analytical formulations for system variables, such as temperature and thermal stress, were derived using the Laplace transform method. This was done considering the effects of laser pulses, non‐local actuators, and fractional actuators. The findings of these investigations are showcased through numerical illustrations and visual representations. The research also included comparisons between the acquired results and those derived from earlier theories, which may be regarded as a specific instance. Validating the suggested model and showing its correctness and applicability is seen as a crucial step. [ABSTRACT FROM AUTHOR]

This study primarily seeks to expand upon these developments by encompassing neutral differential equations of mixed type, incorporating both delay and advanced terms, particularly in the case of the canonical operator. The presented results are derived from the application of the comparison method, Riccati transformation, and integral averaging technique. These methodologies lead to substantial improvements and extensions of existing results found in the literature. Additionally, illustrative examples are provided to demonstrate the practical implications of the developed criteria. [ABSTRACT FROM AUTHOR]

The main aim of this study was to apply an analytical method to solve a nonlinear system of fractional differential equations (FDEs). This method is the Adomian decomposition method (ADM), and a comparison between its results was made by using a numerical method: Runge-Kutta 4 (RK4). It is proven that there is a unique solution to the system. The convergence of the series solution is given, and the error estimate is also proven. After that, the susceptible-infected-recovered (SIR) model was taken as an real phenomenon with such systems. This system is discussed with three different fractional derivatives (FDs): the Caputo-Fabrizio derivative (CFD), the Atangana-Baleanu derivative (ABD), and the Caputo derivative (CD). A comparison between these three different derivatives is given. We aimed to see which one of the new definitions (ABD and CFD) is close to one of the most important classical definitions (CD). [ABSTRACT FROM AUTHOR]

In this work, new oscillation criteria are established for a second-order differential equation with several sublinear neutral terms and in the canonical case. To determine the oscillation conditions, we followed the Riccati approach and also compared the studied equation with a first-order delay equation. Obtaining the oscillation conditions required deducing some new relationships linking the solution to the corresponding function as well as its derivatives. The paper addresses some interesting analytical points in the study of the oscillation of equations with several sublinear neutral terms. These new findings complement some well-known findings in the literature. Furthermore, an example is provided to show the importance of the results. [ABSTRACT FROM AUTHOR]

This paper presents an investigation into the qualitative behavior of solutions for a specific class of fourth-order half-linear neutral differential equations. The main objective of this study is to improve the relationship between the solution and its corresponding function. By developing improved relationships, a novel criterion is proposed to determine the oscillatory behavior of the studied equation. The exclusion of positive solutions is achieved through a comparative approach in which the examined equation is compared to second-order equations. Additionally, the significance of the obtained results is demonstrated by applying them to various illustrative examples. [ABSTRACT FROM AUTHOR]

This paper delves into the analysis of oscillation characteristics within third-order quasilinear delay equations, focusing on the canonical case. Novel sufficient conditions are introduced, aimed at discerning the nature of solutions—whether they exhibit oscillatory behavior or converge to zero. By expanding the literature, this study enriches the existing knowledge landscape within this field. One of the foundations on which we rely in proving the results is the symmetry between the positive and negative solutions, so that we can, using this feature, obtain criteria that guarantee the oscillation of all solutions. The paper enhances comprehension through the provision of illustrative examples that effectively showcase the outcomes and implications of the established findings. [ABSTRACT FROM AUTHOR]

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution x s to its corresponding function z s and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations. [ABSTRACT FROM AUTHOR]

We investigate the oscillation of the fourth-order differential equation for a class of functional differential equations of the neutral type. We obtain a new single-oscillation criterion for the oscillation of all the solutions of our equation. We establish new monotonic properties for some cases of positive solutions of the studied equation. Moreover, we improve these properties by using an iterative method. This development of monotonic properties contributes to obtaining new and more efficient criteria for verifying the oscillation of the equation. The results obtained extend and improve previous findings in the literature by using an Euler-type equation as an example. The importance of the results was clarified by applying them to some special cases of the studied equation. The fourth-order delay differential equations have great practical importance due to their wide applications in civil, mechanical, and aeronautical engineering. Research on this type of equation is still ongoing due to its remarkable importance in many fields. [ABSTRACT FROM AUTHOR]

In this study, the Moore–Gibson–Thompson (MGT) concept of thermal conductivity is applied to a two-dimensional elastic solid in the form of a half-space. This model was constructed using Green and Naghdi's thermoelastic model to address the infinite velocity problem of heat waves. It has been taken into account that the free surface of the medium is immersed in an electromagnetic field of constant intensity, undergoes thermal shock, and rotates with a uniform angular velocity. The governing equations of a modified version of Ohm's law account for the impact of temperature gradients and charge densities. By using the method of normal mode analysis, an analytical representation of the studied physical fields was obtained. The effect of rotation and the modulus of modified Ohm's law on the responses of the field distributions examined is discussed, along with accompanying graphical representations. Other thermoelastic models have been compared with the results of the proposed system when the relaxation time is ignored. [ABSTRACT FROM AUTHOR]

The purpose of this research is to investigate the asymptotic and oscillatory characteristics of odd-order neutral differential equation solutions with multiple delays. The relationship between the solution and its derivatives of different orders, as well as their related functions, must be understood in order to determine the oscillation terms of the studied equation. In order to contribute to this subject, we create new and significant relationships and inequalities. We use these relationships to create conditions in which positive and N-Kneser solutions of the considered equation are excluded. To obtain these terms, we employ the comparison method and the Riccati technique. Furthermore, we use the relationships obtained to create new criteria, so expanding the existing literature on the field. Finally, we provide an example from the general case to demonstrate the results' significance. The findings given in this work provide light on the behavior of odd-order neutral differential equation solutions with multiple delays. [ABSTRACT FROM AUTHOR]

In this article, we investigate some of the qualitative properties of a class of fourth-order neutral differential equations. We start by obtaining new inequalities and relations between the solution and its corresponding function, as well as with its derivatives. The new relations allow us to improve the monotonic and asymptotic properties of the positive solutions of the studied equation. Then, using an improved approach, we establish new criteria that test the oscillation of all solutions. We also rely on the principle of symmetry between positive and negative solutions to obtain the new criteria. The paper provides illustrative examples that highlight the significance of our findings. [ABSTRACT FROM AUTHOR]

In this study, the effects of laser light on the heat transfer of a thin beam heated by an applied current and voltage are investigated. Laser heating pulses are simulated as endogenous heat sources with discrete temporal properties. The heat conduction equation is developed using the energy conservation equation and the modified Moore–Gibson–Thompson (MGT) heat flow vector. Thermal and structural analysis of Euler–Bernoulli microbeams is provided with the support of visco-Pasternak's base with three parameters. Using the Laplace transform method, an approximation of an analytical solution is found for the field variables being examined. A comparison was made of the impacts of laser pulse length, the three foundation coefficients, and the thermal parameters on the responses to changes in measured thermophysical fields, such as deflection and temperature. [ABSTRACT FROM AUTHOR]

In this work, we prove several new (γ, a)-nabla Bennett and Leindler dynamic inequalities on time scales. The results proved here generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using integration by parts, chain rule and Hölder inequality for the (γ, a)-nablafractional derivative on time scales. [ABSTRACT FROM AUTHOR]

In this article, we will prove some new diamond alpha Hilbert-type dynamic inequalities on time scales which are defined as a linear combination of the nabla and delta integrals. These inequalities extend some known dynamic inequalities on time scales, and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proven by using some algebraic inequalities, diamond alpha Hölder inequality, and diamond alpha Jensen's inequality on time scales. [ABSTRACT FROM AUTHOR]

In this paper, we establish oscillation theorems for all solutions to fourth-order neutral differential equations using the Riccati transformation approach and some inequalities. Some new criteria are established that can be used in cases where known theorems fail to apply. The approach followed depends on finding conditions that guarantee the exclusion of positive solutions, and as a result of the symmetry between the positive and negative solutions of the studied equation, we therefore exclude negative solutions. An illustrative example is given. [ABSTRACT FROM AUTHOR]

In the literature, different types of algorithms that are organised to encrypt and decrypt images have been introduced. Some of these depend on chaotic systems where bifurcation routes to chaos exist. Those algorithms have advantages and disadvantages so far as their security level and computational speed are concerned. This study proposes a robust algorithm based on a pixel shuffling and a one‐dimensional chaotic economic map for encrypting and decrypting images. The proposed algorithm is implemented on many images. The security and performance of the proposed method are analysed thoroughly by using key space, key‐sensitivity, correlation of two adjacent pixels, information entropy, contrast and differential attack. On the basis of the obtained experimental results, the proposed algorithm is characterised by a large size of key space, a high sensitivity to the secret key, very low correlation coefficients, a good information entropy and a high contrast. Finally, the experiments are confirmed that the proposed algorithm can resist statistical and differential attacks with high efficiency. [ABSTRACT FROM AUTHOR]

The primary goal of this research is to prove some new Hardy-type ∇-conformable dynamic inequalities by employing product rule, integration by parts, chain rule and (γ , a) -nabla Hölder inequality on time scales. The inequalities proved here extend and generalize existing results in the literature. Further, in the case when γ = 1 , we obtain some well-known time scale inequalities due to Hardy inequalities. Many special cases of the proposed results are obtained and analyzed such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities and new classical conformable fractional integral inequalities. [ABSTRACT FROM AUTHOR]

Efficient and accurate estimations of unidentified parameters of photovoltaic (PV) models are essential to their simulation. This study suggests two new variants of the whale optimization algorithm (WOA) for identifying the nine parameters of the three-diode PV model. The first variant abbreviated as RWOA is based on integrating the WOA with ranking methods under a novel updating scheme to utilize each whale within the population as much as possible during the optimization process. The second variant, namely HWOA, has been based on employing a novel cyclic exploration-exploitation operator with the RWOA to promote its local and global search for averting stagnation into local minima and accelerating the convergence speed in the right direction of the near-optimal solution. Experimentally, RWOA and HWOA are validated on a solar cell (RTC France) and two PV modules (Photowatt-PWP201 and Kyocera KC200GT). Further, these proposed variants are compared with five well-known parameter extraction models in order to demonstrate their notable advantages over the other existing competing algorithms for minimizing the root mean squared error (RMSE) between experimentally measured data and estimated one. The experimental findings show that RWOA is superior in some observed cases and superior in the other cases in terms of final accuracy and convergence speed; yet, HWOA is superior in all cases. [ABSTRACT FROM AUTHOR]

The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map's basins of attraction that includes lobes regions. [ABSTRACT FROM AUTHOR]

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game's dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained. [ABSTRACT FROM AUTHOR]

We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give any advantages but affects the stability of the game's equilibrium points. Theoretically, we prove that the equilibrium points can be destabilized through Neimark-Sacker followed by flip bifurcation. Numerically, we prove that the map describing the game is noninvertible and gives rise to several stable attractors (multistability). Furthermore, the dynamics of the map give different shapes of quite complicated attraction basins of periodic cycles. [ABSTRACT FROM AUTHOR]

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game's map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game's parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game's map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case. [ABSTRACT FROM AUTHOR]

In the literature, there are many image encryption algorithms that have been constructed based on different chaotic maps. However, those algorithms do well in the cryptographic process, but still, some developments need to be made in order to enhance the security level supported by them. This paper introduces a new cryptographic algorithm that depends on a logistic and two-dimensional chaotic economic map. The robustness of the introduced algorithm is shown by implementing it on several types of images. The implementation of the algorithm and its security are partially analyzed using some statistical analyses such as sensitivity to the key space, pixels correlation, the entropy process, and contrast analysis. The results given in this paper and the comparisons performed have led us to decide that the introduced algorithm is characterized by a large space of key security, sensitivity to the secret key, few coefficients of correlation, a high contrast, and accepted information of entropy. In addition, the results obtained in experiments show that our proposed algorithm resists statistical, differential, brute-force, and noise attacks. [ABSTRACT FROM AUTHOR]