In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton's polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.
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http://dx.doi.org/10.1038/s41598-024-77567-4 | DOI Listing |
Phys Rev E
November 2024
Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California 90089-2531, USA.
Statistics of diffusion, modeled by random walks, such as the mean number of distinct sites visited S(t) at time t, the mean probability P_{0}(t) of being at the origin of the walk, and the mean-squared displacements 〈R^{2}(t)〉 of the random walkers have been studied extensively in the past in both regular lattices and such disordered media as percolation clusters and other fractal structures, and universal power laws for such quantities have been derived. S(t) provides insight into reaction properties of geological formations, while P_{0}(t) is directly linked with the problem of back diffusion in remediation of groundwater aquifers. In all such studies, it was assumed that the conductances of the bonds that connect nearest-neighbor sites of the lattices are equal.
View Article and Find Full Text PDFMethodsX
June 2024
Department of Mathematics, Near East Boulevard, Mathematics Research Center, Near East University, PC: 99138, Mersin, Nicosia 10, Turkey.
Numerous special functions, including the beta function, hypergeometric functions, and other orthogonal polynomials, are closely connected to the gamma function. Recently, gamma function has been enhanced by adding a new parameter. As a consequence, this gamma is called the parametric gamma function or b-gamma function.
View Article and Find Full Text PDFNanomaterials (Basel)
November 2024
Department of Mathematics and Physics, University of Campania "Luigi Vanvitelli", 81100 Caserta, Italy.
Nanofluids have improved thermophysical properties compared to conventional fluids, which makes them promising successors in fluid technology. The use of nanofluids enables optimal thermal efficiency to be achieved by introducing a minimal concentration of nanoparticles that are stably suspended in conventional fluids. The use of nanofluids in technology and industry is steadily increasing due to their effective implementation.
View Article and Find Full Text PDFComput Biol Med
January 2025
Future Technology Research Center, National Yunlin University of Science and Technology, Douliu, Yunlin, 64002, Taiwan. Electronic address:
Within the intricate fabric of human physiology, cholesterol, a lipid present in cell membranes exerts a discernible effect on the concentration of the drug in human body that influence the aspects of drug pharmacokinetics. The objective of this work is to design a case study based fractional order cholesterol drug interaction model that encapsulates the nuanced dynamics inherent in the multifaceted human physiology with identification of essential variables including drug concentration K and cholesterol level γ. The strength of nonlinear autoregressive with exogenous inputs (NARX) neural networks are exploited to predict the temporal dynamics that reveal the hidden intricacies and subtle patterns within the fractional model.
View Article and Find Full Text PDFSci Rep
November 2024
Mechatronics Department, Faculty of Engineering, University of Debrecen, Ótemető u. 4-5, Debrecen, 4028, Hungary.
Reformulating the physical processes associated with the evolution of different ailments in accordance with globally shared objectives is crucial for deeper comprehension. This study aims to investigate the mechanism by which the HB virus induces harmful inflammation of the liver, with a focus on early detection and therapy using corticosteroids or chemotherapy. Based on the developed hypothesis, a new mathematical model has been created for this purpose.
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