This paper investigates the well-posedness and positivity of solutions to a class of delayed transport equations on a network. The material flow is delayed at the vertices and along the edges. The problem is reformulated as an abstract boundary delay equation, and well-posedness is proved by using the Staffans–Weiss theory. We also establish spectral theory for the associated delay operators and provide conditions for the positivity of the semigroup.
This paper is concerned with the existence of positive solutions for a class of Schrödinger-Bopp-Podolsky systems in three-dimensional Euclidean space. The system couples a nonlinear Schrödinger equation with a fourth-order elliptic equation governing the electrostatic potential. We establish existence under assumptions on an external potential, which is allowed to vanish at infinity, and on a nonlinearity with subcritical growth. A key feature of our work is demonstrating that existence hinges on a delicate interplay between the decay rate of the potential and the local behavior of the nonlinearity near the origin. The proof relies on variational methods. We employ a penalization technique to overcome the lack of compactness, establish the existence of a solution for the resulting auxiliary problem via the Mountain Pass Theorem, and use crucial -estimates to show this solution solves the original system for a suitable range of parameters.
RETRACTION: Y. Xu, Q. Nguyen, O. Malekahmadi, R. Hadi, Z. Jokar, A. Mardani, A. Karimipour, R. Ranjbarzadeh, Z. Li, Q.-V. Bach, “Synthesis And Characterization Of Additive Graphene Oxide Nanoparticles Dispersed In Water: Experimental And Theoretical Viscosity Prediction Of Non-Newtonian Nanofluid”, Mathematical Methods in the Applied Sciences (Early View): https://doi.org/10.1002/mma.6381.
The above article, published online on 05 April 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor-in-Chief, Wolfgang Sprößig; and John Wiley & Sons Ltd. The article was submitted as part of a guest-edited special issue. As part of an investigation, the journal discovered that the article was accepted solely on the basis of compromised editorial handling and what appears to be a manipulated peer review process. When informed of the decision to retract the article, the institution which was listed as the affiliation for five of the authors noted that four of them were never affiliated with the institution, and that the department noted in the affiliations (the Department of Mechanical Engineering, University of Rome, Sapienza, Italy) does not exist. As a result, the data and conclusions are considered unreliable, and the accountability of the authorship is considered compromised. Therefore the article must be retracted. Author R. Ranjbarzadeh has been informed of the retraction and stated that his involvement with the research was limited to part of the experimental measurements, and that he was not involved in the data analysis, writing, or submission of the manuscript. The corresponding author has agreed that author R. Ranjbarzadeh's role in the production of the data and article was limited to taking basic laboratory measurements.
RETRACTION: T.A. Alkanhal, “Establishing artificial neural network to investigate thermal properties of carbon nanotube/zinc oxide composite dispersed in water”, Mathematical Methods in the Applied Sciences (Early View): https://doi.org/10.1002/mma.7138.
The above article, published online on 06 February 2021 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor-in-Chief, Wolfgang Sprößig; and John Wiley & Sons Ltd. The article was submitted as part of a guest-edited special issue. Following publication, it has come to the attention of the journal that the article was accepted solely on the basis of compromised editorial handling and peer review processes. As a result, the data and conclusions are considered unreliable, therefore the article must be retracted.
RETRACTION: N.H. Abu-Hamdeh, “Improving Energy Storage And Performance Through Implementing Artificial Neural Network Modeling To Forecast Heat Transfer And Entropy Generation Within A Wavy-Wall Microchannel Under Discontinuous-Boundary Condition–Hybrid Nanofluid Utilization”, Mathematical Methods in the Applied Sciences (Early View): https://doi.org/10.1002/mma.7319.
The above article, published online on 31 May 2021 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor-in-Chief, Wolfgang Sprößig; and John Wiley & Sons Ltd. The article was submitted as part of a guest-edited special issue. Following publication, it has come to the attention of the journal that the article was accepted solely on the basis of compromised editorial handling and peer review processes. As a result, the data and conclusions are considered unreliable, therefore the article must be retracted. When informed of the decision, the authors have disagreed with the decision to retract.
RETRACTION: Q. Nguyen, P. Ghorbani, S.A. Bagherzadeh, O. Malekahmadi, A. Karimipour, “Performance Of Joined Artificial Neural Network And Genetic Algorithm To Study The Effect Of Temperature And Mass Fraction Of Nanoparticles Dispersed In Ethanol”, Mathematical Methods in the Applied Sciences (Early View): https://doi.org/10.1002/mma.6688.
The above article, published online on 17 August 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor-in-Chief, Wolfgang Sprößig; and John Wiley & Sons Ltd. The article was submitted as part of a guest-edited special issue. Following publication, it has come to the attention of the journal that the article was accepted solely on the basis of compromised editorial handling and peer review processes. As a result, the data and conclusions are considered unreliable, therefore the article must be retracted.
RETRACTION: A. Din, and Y. Li, “Stochastic Optimal Analysis For The Hepatitis B Epidemic Model With Markovian Switching”, Mathematical Methods in the Applied Sciences (Early View): https://doi.org/10.1002/mma.8218.
The above article, published online on 12 March 2022 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor-in-Chief, Wolfgang Sprößig; and John Wiley & Sons Ltd. The article was submitted as part of a guest-edited special issue. Following publication, it has come to the attention of the journal that the article was accepted solely on the basis of compromised editorial handling and peer review processes. As a result, the data and conclusions are considered unreliable, therefore the article must be retracted. When informed of the decision, the authors have disagreed with the decision to retract.
This study presents a novel fractal–fractional model to investigate the dynamics of drug addiction within a specific region, capturing memory-driven behaviors and complex interactions among different subpopulations of drug users. The model employs fractal–fractional differential equations with a nonsingular and nonlocal kernel, enabling an accurate representation of long-term dependencies and the chronic nature of addiction. We conduct a theoretical analysis to establish the existence and stability of drug-free and persistent drug-use equilibria, highlighting the role of historical exposure and social influence in shaping addiction dynamics. Numerical solutions are obtained using the Adams–Bashforth method adapted for fractal–fractional derivatives, ensuring computational efficiency despite the memory effects introduced by the model. Simulations illustrate the progression of light, hidden, and treated drug users, as well as recovered individuals, providing insights into the effectiveness of early interventions, rehabilitation programs, and relapse prevention strategies. Overall, the proposed framework offers a robust tool for understanding addiction dynamics and informing public health policies aimed at mitigating the impact of substance abuse in communities.
RETRACTION: T. Elnaqeeb, N.A. Shah, A. Rauf, “Natural Convection Flows Of Carbon Nanotube Prabhakar-Like Fractional Second-Grade Nanofluids Over an Infinite Plate With Newtonian Heating”, Mathematical Methods in the Applied Sciences (Early View): https://doi.org/10.1002/mma.6795.
The above article, published online on 05 August 2020 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the journal Editor-in-Chief, Wolfgang Sprößig; and John Wiley & Sons Ltd. The article was submitted as part of a guest-edited special issue. Following publication, it has come to the attention of the journal that the article was accepted solely on the basis of compromised editorial handling and peer review processes. As a result, the data and conclusions are considered unreliable, therefore the article must be retracted. When informed of the decision, the authors have disagreed with the decision to retract.
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