2026-03-05
Liliana Guran, Muhammad Suhail Aslam, Mohammad Showkat Rahim Chowdhury, Thabet Abdeljawad
In this paper, we introduce the concepts of (α − Θ)-contraction and Reich-type contraction within the framework of complex valued-controlled metric spaces (CVCMS). We also present related fixed point theorems for CVCMS, building on the works considered in the literature review for controlled metric type spaces. To demonstrate the practical implications and significance of our results, we provide several examples and an application in dynamic programming.
2026-03-05
Christophe Chesneau
This article focuses on a particular Hardy-Hilbert-type integral inequality defined in the entire plane. Its innovation lies in its use of a ratio-cosine kernel function, setting it apart from most existing literature on the subject. As a consequence of the main theorem, a related integral inequality of independent interest is also derived. The exposition is self-contained, with full details of all proofs presented and each step carefully justified.
2026-03-05
Isha Zahid, Umar Raza, Mohsan Raza
Let \(\mathcal{S}_{cos}^{\ast }\) be the subclass of starlike functions \(f\) associated with cosine function defined by \(\left( zf^{\prime }(z)/f(z)\right) \prec \cos (z)\). In this paper, we obtain the sharp coefficient bounds and Hankel determinants of second order for the inverse logarithmic function for this class. We also present the best possible bounds of second order Toeplitz determinant for the functions in the same class.
2026-03-05
Karim Benalia, Karim Beddek, Thiziri Sifaoui, Brahim Oukacha
This paper presents a new computational method based on the Picard iteration method for solving boundary optimal control problems governed by parabolic partial differential equations with two-point boundary conditions. The proposed approach adapts the Picard iteration method to solve the necessary optimality conditions derived from Pontryagin’s minimum principle, yielding a solution expressed as a truncated power series. To evaluate the effectiveness of the proposed method, a numerical example is provided, and the obtained results are compared with those derived from an alternative approach, demonstrating the accuracy and reliability of the method.
2026-03-05
Mykola Ivanovich Yaremenko
We establish the generalized parametric logarithmic Sobolev inequalities in the Gagliardo-Nirenberg form for variable exponential space with log Holder exponential function. Employing the generalized parametric logarithmic Sobolev inequalities, we establish the existence of weak solutions to the boundary problem for the hyperbolic equation with logarithmic nonlinearity and involving variable exponents.
2026-03-05
Boukary Ouedraogo, Nour Eddine Alaa, Elisée Gouba, Soumaye HARO
Although national and international institutions, such as the World Health Organization (WHO) and UNAIDS, are making significant efforts to eradicate HIV by 2030, it remains a major threat to global public health. Despite its low prevalence, HIV continues to claim lives and remains a major public health issue, especially in developing countries. Thanks to the accessibility of antiretroviral drugs, the prevalence of this scourge has been gradually declining worldwide in recent years. Thus, the present article investigates antiretroviral therapy's effectiveness in controlling viral transmission through a fractional-order extension of a deterministic model. We study the boundedness of the model's solution by applying the Laplace transform to solve the fractional Gronwall inequality. To ensure the existence and uniqueness of the model's solution, we rely on the Picard-Lindelöf theorem. We also study the stability of the disease-free equilibrium point to qualitatively analyze the behavior of the model. Next, we perform a sensitivity analysis of the basic reproduction number $\mathcal{R}_0$ to evaluate its robustness concerning the model parameters. Finally, we simulate the approximate solutions of the fractional-order model in MATLAB for different values of the fractional order and present the results of the sensitivity analysis and numerical simulation. Our results demonstrate that the fractional model provides real added value in modeling, thanks to its ability to incorporate memory effects and finely tune transmission dynamics according to the fractional order, thereby allowing for a more realistic representation of epidemiological processes.
2025-12-03
Anass Lamaizi, Mahmoud El Ahmadi, Mohammed Barghouthe, Omar Darhouche
In this paper, we are interested to study the weak solutions for the following nonlinear parabolic problem: \[ \begin{cases} u_t - \Delta_p u + \vert u \vert^{p-2} u = 0 \quad \text{ in } ~ \Omega ,~ t>0 , \\ \vert \nabla u \vert^{p-2} \frac{\partial u}{\partial \nu }= g(u) \quad \quad \quad ~~ \text{ on }~ \partial \Omega ,~ t>0 , \\ u(x;0)=u_0 (x) \quad \quad \quad \quad ~~~~ \text{ in } ~ \Omega . \end{cases} \] Using the Galerkin approximation and a family of potential wells, we establish the existence of global weak solution under appropriate conditions. Additionally, we provide a result on the blow-up and asymptotic behavior of certain solutions with positive initial energy.
2025-12-03
Bilel Elgabeur
In this article, we study the essential pseudospectra by measure of polynomially strict singular operators, which is a generalization of the class of strict singular operators. We present some new results in essential pseudospectra for closed linear operators in Banach space with polynomially strict singular operators. Furthermore, we apply the obtained results to analyze the incidence of some perturbation results on left(resp. right) Weyl essential pseudospectra and left(resp. right) Fredholm essential pseudospectra. In addition, we will describe the essential pseudospectra of a sum of two bounded linear operators. A final application of the obtained results is to characterize the pseudo-left (right)-Fredholm spectra of 2 x 2 block operator matrices. TRANSLATE with x English Arabic Hebrew Polish Bulgarian Hindi Portuguese Catalan Hmong Daw Romanian Chinese Simplified Hungarian Russian Chinese Traditional Indonesian Slovak Czech Italian Slovenian Danish Japanese Spanish Dutch Klingon Swedish English Korean Thai Estonian Latvian Turkish Finnish Lithuanian Ukrainian French Malay Urdu German Maltese Vietnamese Greek Norwegian Welsh Haitian Creole Persian TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster Portal Back
2025-12-03
Mohamed El Hathout, Houda Fahim, Nour Eddine Alaa
The aim of this work is to study the existence and uniqueness of integral solutions for a class of non-local parabolic equations. There are two main results. First, we use a subdifferential technique to verify the existence and uniqueness of weak solutions when the initial data belong to \(L^2\). Secondly, the existence and uniqueness of an integral solution is demonstrated by extending the study to initial data in \(L^1\) space. To overcome the difficulties caused by non-local terms, the proposed strategy combines new approaches with sophisticated strategies derived from the theory of accretive operators. Non-local evolution equations and their applications are better understood thanks to these results.
2025-02-24
Saf Salim, Touil Nadji, Abita Rahmoune
We study the solvability of a class of quasilinear elliptic equations with \((p(x),k(x))\)-growth structure and with nonlinear boundary conditions in the context of Kelvin-Voigt damping with arbitrary data. We approach our problem in a suitable functional classes by considering the so-called Lebesgue and Sobolev spaces with variable exponents. In the first step we establish existence and uniqueness results of solutions for the considered model if the data are regular enough. Our main idea is essentially based on using fixed point theory and Faedo-Galerkin approaches and includes some new techniques. Second, we assume the data is large enough and show that the energy grows exponentially.
2025-02-24
Elidrrissi Erriahi Ghita, Elhoussine Azroul, Abdelilah Lamrani Alaoui
In this paper, we prove the existence of a weak solution to the following nonlinear periodic parabolic equations in Orlicz-spaces: ∂u/∂t− div(a(x,t,∇u)) = f(x, t) where −div(a(x, t,∇u)) is a Leray-Lions operator defined on a subset of \(W^{1,x}_{0} L_{M}(Q)\). The Δ2-condition is not assumed and the data f belongs to \(W{−1,x}E_{\overline{M}}(Q)\). The Galerkin method and the fixed point argument are employed in the proof.