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Explicit travelling wave solutions to the time fractional Phi-four equation and their applications in mathematical physics.
Sci Rep
January 2025
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia.
In applied research, fractional calculus plays an important role for comprehending a wide range of intricate physical phenomena. One of the Klein-Gordon model's peculiar case yields the Phi-four equation. Additionally, throughout the past few decades it has been utilized to explain the kink and anti-kink solitary waveform contacts that occur in biological systems and in the field of nuclear mechanics.
View Article and Find Full Text PDFFractional and stochastic modeling of breast cancer progression with real data validation.
PLoS One
January 2025
Biology Department, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia.
This study presents a novel approach to modeling breast cancer dynamics, one of the most significant health threats to women worldwide. Utilizing a piecewise mathematical framework, we incorporate both deterministic and stochastic elements of cancer progression. The model is divided into three distinct phases: (1) initial growth, characterized by a constant-order Caputo proportional operator (CPC), (2) intermediate growth, modeled by a variable-order CPC, and (3) advanced stages, capturing stochastic fluctuations in cancer cell populations using a stochastic operator.
View Article and Find Full Text PDFEconomic analysis of hemodialysis and urgent-start peritoneal dialysis therapies.
J Bras Nefrol
January 2025
Universidade Estadual Paulista, Faculdade de Medicina, Departamento de Clínica Médica, Botucatu, SP, Brazil.
Introduction: Unplanned initiation of renal replacement therapy (RRT) in chronic kidney disease (CKD) patients is a common situation worldwide. In this scenario, peritoneal dialysis (PD) has emerged as a therapeutic option compared to hemodialysis (HD). In planned RRT, the costs of PD are lower than those of HD; however, the literature lacks such analyses when initiation is urgent.
View Article and Find Full Text PDFUnderstanding the independent samples t test in nursing research.
Br J Nurs
January 2025
Associate Professor, Nursing and Midwifery, University of Limerick, Limerick, Ireland.
Critical thinking is required for successful nursing outcomes. For evidence-based practice, there is a need to understand and apply quantitative methods of research and statistical analysis in order to obtain evidence. However, the literature shows that the use of quantitative methods among nurse researchers can be problematic.
View Article and Find Full Text PDFNonlinear dynamic wave properties of travelling wave solutions in in (3+1)-dimensional mKdV-ZK model.
PLoS One
January 2025
Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.
The (3+1)-dimensional mKdV-ZK model is an important framework for studying the dynamic behavior of waves in mathematical physics. The goal of this study is to look into more generic travelling wave solutions (TWSs) for the generalized ion-acoustic scenario in three dimensions. These solutions exhibit a combination of rational, trigonometric, hyperbolic, and exponential solutions that are concurrently generated by the new auxiliary equation and the unified techniques.
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