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We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional. [ABSTRACT FROM AUTHOR]

This manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ -Caputo fractional derivatives. The application of Banach's fixed-point theorem (BFPT) ensures the uniqueness of the solutions, while Schauder's fixed-point theorem (SFPT) is instrumental in determining the existence of these solutions. Furthermore, we assess the stability of the proposed equation using the Ulam–Hyers stability criterion. To illustrate our results, we provide a concrete example showcasing their practical implications. [ABSTRACT FROM AUTHOR]

The main goal of this article is to obtain the existence of solutions for a nonlinear system of a coupled Petrovsky–Petrovsky system in the presence of infinite memories under minimal assumptions on the functions g 1 , g 2 and φ 1 , φ 2 . Here, g 1 , g 2 are relaxation functions and φ 1 , φ 2 represent the sources. Also, a general decay rate for the associated energy is established. Our work is partly motivated by recent results, with a necessary modification imposed by the nature of our problem. In this work, we limit our results to studying the system in a bounded domain. The case of the entire domain R n requires separate consideration. Of course, obtaining such a result will require not only serious technical work but also the use of new techniques and methods. In particular, one of the most significant points in achieving this goal is the use of the perturbed Lyapunov functionals combined with the multiplier method. To the best of our knowledge, there is no result addressing the linked Petrovsky–Petrovsky system in the presence of infinite memory, and we have overcome this lacune. [ABSTRACT FROM AUTHOR]

This article deals with a non-classical model, namely a thermoelastic laminated beam along with microtemperature effects, nonlinear delay, and nonlinear structural damping, where the last two terms both affect the equation which depicts the dynamics of slip. With the help of convenient conditions in both weight delay and wave speeds, we demonstrate explicit and general energy decay rates of the solution. To attain our interests, we highlight useful properties regarding convex functions and apply a specific approach known as the multiplier technique, which enables us to prove the stability results. Our results here aim to show the impact of different types of damping by taking into account the interaction between them, which extends recent publications in the literature. [ABSTRACT FROM AUTHOR]

We answer some questions in a paper by Kaneko and Koike ['On modular forms arising from a differential equation of hypergeometric type', Ramanujan J.7(1–3) (2003), 145–164] about the modularity of the solutions of a certain differential equation. In particular, we provide a number-theoretic explanation of why the modularity of the solutions occurs in some cases and does not occur in others. This also proves their conjecture on the completeness of the list of modular solutions after adding some missing cases. [ABSTRACT FROM AUTHOR]

This paper concerns the study of the Schwartz differential equation { h , τ } = s ⁢ E 4 ⁡ (τ) {\{h,\tau\}=s\operatorname{E}_{4}(\tau)} , where E 4 {\operatorname{E}_{4}} is the weight 4 Eisenstein series and s is a complex parameter. In particular, we determine all the values of s for which the solutions h are modular functions for a finite index subgroup of SL 2 ⁡ (ℤ) {\operatorname{SL}_{2}({\mathbb{Z}})}. We do so using the theory of equivariant functions on the complex upper-half plane as well as an analysis of the representation theory of SL 2 ⁡ (ℤ) {\operatorname{SL}_{2}({\mathbb{Z}})}. This also leads to the solutions to the Fuchsian differential equation y ′′ + s ⁢ E 4 ⁡ y = 0 {y^{\prime\prime}+s\operatorname{E}_{4}y=0}. [ABSTRACT FROM AUTHOR]

In this manuscript, we generalise previous results in the literature by providing sufficient conditions for the matrix measure to guarantee the stability, asymptotic stability and exponential stability of a neutral system of differential equations. This is achieved by constructing a suitable operator from our system and applying the Banach fixed point theorem. [ABSTRACT FROM AUTHOR]

For any discrete group Γ and any two-dimensional complex representation ρ of Γ, we introduce the notion of ρ-equivariant functions, and we show that they are parametrized by vector-valued modular forms. We also provide examples arising from the monodromy of differential equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the critical points of classical modular forms. In particular, we prove that for each modular form f for a subgroup of , its derivative has infinitely many inequivalent zeros and all, but a finite number, are simple. [Copyright &y& Elsevier]

The application of artificial intelligence (AI) in predictive analytics is growing in popularity. It has the power to offer ground-breaking solutions for a range of social problems and real world societal difficulties. It is helpful in addressing some of the social issues that today's world seems incapable of solving. One of the most significant phenomena affecting people's lives is divorce. The goal of this paper is to study the use of machine learning algorithms to determine the effectiveness of divorce predictor scale (DPS) and identify the reasons that usually lead to divorce in the scenario of Hail region, KSA. For this purpose, in this study, the DPS, based on Gottman couples therapy, was used to predict divorce by applying different machine learning algorithms. There were 54 items of the DPS used as features or attributes for data collection. In addition to the DPS, a personal information form was utilized to gather participants' personal data in order to conduct this study in a more structured and traditional manner. Out of 148 participants 116 participants were married whereas 32 were divorced. With the use of algorithms artificial neural network (ANN), naïve bayes (NB), and random forest (RF), the effectiveness of DPS was examined in this study. The correlation based feature selection method was used to identify the top six features from the same dataset and the highest accuracy rate was 91.66% with RF. The results show that DPS can predict divorce. This scale can help family counselors and therapists in case formulation and intervention plan development process. Additionally, it may be argued that the Hail region, KSA sampling confirmed the Gottman couples treatment predictors. [ABSTRACT FROM AUTHOR]

A certain class of nonlinear differential equations representing a generalized Van der Pol oscillator is proposed in which we study the behavior of the existing solution. After using the appropriate variables, the first Levinson's change converts the equations into a system with two equations, and the second converts these systems into a Lipschitzian system. Our main result is obtained by applying the Second Bogolubov's Theorem. We established some integrals, which are used to compute the average function of this system and arrive at a new general condition for the existence of an asymptotically stable unique periodic solution. One of the well-known results regarding asymptotic stability appears, owing to the Second Bogolubov's Theorem, and the advantage of this method is that it can be applied not only in the periodic dynamical systems, but also in non-almost periodic dynamical systems. [ABSTRACT FROM AUTHOR]

The paper is devoted to the problem of the local existence for a solution to a nonlinear wave equation, with the dissipation given by a nonlinear form with the presence of a nonlinear memory term. Moreover, the global nonexistence of a solution is established using the test function method. We combine the Fourier transform and fractional derivative calculus to achieve our goal. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new class of nonlinear fractional integrodifferential systems that includes the Ψ -Riemann–Liouville fractional integral term. Using the technique of upper and lower solutions, the solvability of the system is examined. We add two examples to demonstrate and validate the main result. The main results highlight crucial contributions to the general theory of fractional differential equations. [ABSTRACT FROM AUTHOR]

Various scholars have lately employed a wide range of strategies to resolve specific types of symmetrical fractional differential equations. In this paper, we propose a new fractional identity for multiplicatively differentiable functions; based on this identity, we establish some new fractional multiplicative Bullen-type inequalities for multiplicative differentiable convex functions. Some applications of the obtained results are given. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Divorce prediction using machine learning algorithms in Ha'il region, KSA" published in Scientific Reports. The correction addresses an error in the funding section of the original article, where the project number was incorrect. The correct project number is now stated as RD-21 067. The original article has been corrected. The authors of the article are Abdelkader Moumen, Ayesha Shafqat, Tariq Alraqad, Etaf Saleh Alshawarbeh, Hicham Saber, and Ramsha Shafqat. [Extracted from the article]