In this paper, we develop fractal calculus by defining improper fractal integrals and their convergence and divergence conditions with related tests and by providing examples. Using fractal calculus that provides a new mathematical model, we investigate the effect of fractal time on the evolution of the physical system, for example, electrical circuits. In these physical models, we change the dimension of the fractal time; as a result, the order of the fractal derivative changes; therefore, the corresponding solutions also change. We obtain several analytical solutions that are non-differentiable in the sense of ordinary calculus by means of the local fractal Laplace transformation. In addition, we perform a comparative analysis by solving the governing fractal equations in the electrical circuits and using their smooth solutions, and we also show that when α=1, we get the same results as in the standard version.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1063/5.0042813 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Transdermal electrophysiological recordings of diet-induced small fiber peripheral neuropathy using a needle electrode array in mice and man.
Front Bioeng Biotechnol
January 2025
Department of Neurological Surgery, The Ohio State University, Columbus, OH, United States.
Background: Diabetic peripheral neuropathy (DPN) is a common complication of diabetes. Proactive treatment options remain limited, which is exacerbated by a lack of sensitive and convenient diagnostics, especially early in disease progression or specifically to assess small fiber neuropathy (SFN), the loss of distal small diameter axons that innervate tissues and organs.
Methods: We designed, fabricated, tested, and validated a first-of-its-kind medical diagnostic device for the functional assessment of transdermal small fiber nerve activity.
Comprehensive Study on the Thermoelectric Properties and Influencing Factors of Wearable Spiral Bracelets Enhanced by Radiation Cooling.
ACS Omega
January 2025
Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, China.
Wearable thermoelectric generator (TEG) can collect human body heat and convert it into electrical energy, achieving self-powering of the device and thus becoming a hot research topic at present. By utilization of three-dimensional spiral thin-film thermoelectric structures and passive radiation cooling methods, the heat transfer area can be increased and power generation can be enhanced. In order to study the effect of outdoor radiation cooling on the thermoelectric performance of spiral heating, as well as the TEG performance output under different external environments and circuit loads, this paper proposes a new three-dimensional coupled numerical model of the spiral thermoelectric wristband system with multiple physical fields.
View Article and Find Full Text PDFOptically Readable Multilevel Magnetic Memory States in Perpendicularly Exchange-Biased Ferromagnetic Multilayers.
Small
January 2025
Department of Physics, Kyungpook National University, Daegu, 41566, South Korea.
The construction of multilevel magnetic states using materials with perpendicular magnetic anisotropy (PMA) offers a novel approach to enhancing the storage density and read/write efficiency of nonvolatile magnetic memory devices. In this study, optically readable multilevel magnetic domain states are achieved by inducing asymmetric interlayer interactions and decoupling the magnetic reversal behavior of individual ferromagnetic (FM) layers in exchange-biased FM multilayers with PMA. Hepta-level magnetic domain states are formed in [Co/Pt] FM multilayers grown on an antiferromagnetic FeO layer within a relatively low magnetic field range of ∼±400 Oe.
View Article and Find Full Text PDFMulti-objective optimization of the heating oil circuit inside the calendering roller for the lithium battery pole piece.
Sci Rep
January 2025
Xingtai Naknor Technology Co., Ltd, Xingtai, 054000, China.
The heating oil circuit plays an essential role in the heating calendering roller for the lithium battery pole piece. To achieve the optimization of the heating oil circuit, a fluid-thermal-structural coupling method and a multi-objective optimization procedure are proposed to obtain the optimal solution. A fluid-thermal-structural coupling flowchart based on the numerical modeling for the calendering roller temperature distribution is created to automate the analysis processes in the optimization iteration.
View Article and Find Full Text PDFAn optogenetic mouse model of hindlimb spasticity after spinal cord injury.
Exp Neurol
January 2025
Brain and Mind Research Institute, Department of Biology, University of Ottawa, Ottawa, Ontario, Canada. Electronic address:
Spasticity is a common comorbidity of spinal cord injury (SCI), disrupting motor function and resulting in significant discomfort. While elements of post-SCI spasticity can be assessed using pre-clinical SCI models, the robust measurement of spasticity severity can be difficult due to its periodic and spontaneous appearance. Electrical stimulation of sensory afferents can elicit spasticity-associated motor responses, such as spasms; however, placing surface electrodes on the hindlimbs of awake animals can induce stress or encumbrance that could influence the expression of behaviour.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!