Subdiffusive Source Sensing by a Regional Detection Method.

Motivated by the fact that the danger may increase if the source of pollution problem remains unknown, in this paper, we study the source sensing problem for subdiffusion processes governed by time fractional diffusion systems based on a limited number of sensor measurements. For this, we first give some preliminary notions such as source, detection and regional spy sensors, etc. Secondly, we investigate the characterizations of regional strategic sensors and regional spy sensors. A regional detection approach on how to solve the source sensing problem of the considered system is then presented by using the Hilbert uniqueness method (HUM). This is to identify the unknown source only in a subregion of the whole domain, which is easier to be implemented and could save a lot of energy resources. Numerical examples are finally included to test our results

Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions on regional gradient exact and approximate controllability are first given and proved in detail. Secondly, we propose an approach on how to calculate the minimum number of $\omega-$strategic actuators. Moreover, the existence, uniqueness and the concrete form of the optimal controller for the system under consideration are presented by employing the Hilbert Uniqueness Method (HUM) among all the admissible ones. Finally, we illustrate our results by an interesting example.Comment: 16 page

Emerging Current Trends and Research Focus Related to Pancreatic Cancer Metabolism: A Bibliometric and Visualized Analysis

BACKGROUND: As a malignant digestive system tumor, pancreatic cancer has unique metabolic characteristics. In recent years, the study of pancreatic cancer metabolism is in full swing, which provides a new direction for the treatment of pancreatic cancer patients. However, there is no systematic report of pancreatic cancer metabolism. In this paper, bibliometrics and visualization methods were used to analyze the number of publications, countries/regions, authors, institutions, journals, co-cited references, and keywords of pancreatic cancer metabolism articles, to summarize the research trends and predict research hotspots. METHODS: We searched, screened and downloaded articles on pancreatic cancer metabolism through the Web of Science Core Collection (WoSCC). Using CiteSpace, VOSviewer and Bibliometrix Package to analyze publications, countries/regions, authors, institutions, journals, co-cited references, and keywords of pancreatic cancer metabolism to identify research trends and predict research hotspots. RESULTS: According to the inclusion and exclusion criteria, a total of 5,255 articles were retrieved during the period 1943-2022. The number of publications on pancreatic cancer metabolism is increasing year by year. The United States (n=1602, 30.49%), China (n=1074, 20.44%), and Italy (n=313, 5.96%) are the three countries with the largest number of publications and citations, and there is close cooperation between countries. LI J (n=55) is the most prolific author. FUDAN UNIV (n=348) is the most published institution. CANCERS (n=118), PLOS ONE (n=93), and CANCER RESEARCH (n=80) are the most popular journals in this field. Nutriment-deficient environment , cancer chemoprevention and targeting cancer stem cell are the main areas of focus. immunotherapy , ferroptosis and targeted therapy are hot keywords in recent years. Taking pancreatic cancer metabolism as an entry point to study the role of traditional Chinese medicine (TCM) mainly focuses on curcumin and resveratrol, lack of broader and deeper research on TCM. CONCLUSIONS: The number of publications on pancreatic cancer metabolism has generally increased, and scholars have generally paid more attention to this field. immunotherapy , ferroptosis and targeted therapy are the current research hotspots. The in-depth study of pancreatic cancer metabolism will provide new ideas for the treatment of pancreatic cancer

Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < <i>α</i> < 2

This paper is mainly concerned with the asymptotic stability of the solutions of a class of nonlinear fractional differential equations of order 1 α < 2 in a weighted Banach space. By first converting the nonlinear fractional differential equations to ordinary differential equations with a fractional integral perturbation, our main results are obtained via the Banach contraction mapping principle, which surely provides a new way to the stability analysis of nonlinear fractional differential equations. An application is also introduced to validate the above conclusions

Integrated Time-Fractional Diffusion Processes for Fractional-Order Chaos-Based Image Encryption

The purpose of this paper is to explore a novel image encryption algorithm that is developed by combining the fractional-order Chua’s system and the 1D time-fractional diffusion system of order α∈(0,1]. To this end, we first discuss basic properties of the fractional-order Chua’s system and the 1D time-fractional diffusion system. After these, a new spatiotemporal chaos-based cryptosystem is proposed by designing the chaotic sequence of the fractional-order Chua’s system as the initial condition and the boundary conditions of the studied time-fractional diffusion system. It is shown that the proposed image encryption algorithm can gain excellent encryption performance with the properties of larger secret key space, higher sensitivity to initial-boundary conditions, better random-like sequence and faster encryption speed. Efficiency and reliability of the given encryption algorithm are finally illustrated by a computer experiment with detailed security analysis

Approximate controllability of semilinear fractional evolution equations of order <i>α</i>∈(1, 2] with finite delay

This paper considers the approximate controllability of semilinear fractional evolution equations of order α∈ (1, 2] with finite delay. Using the contraction mapping principle, we explore the existence and uniqueness of the mild solution. Furthermore, under certain hypotheses, the approximate controllability is obtained by the theory of strongly continuous-order cosine family. As an illustration of the application of the obtained result, an example is given at last

Subdiffusive Source Sensing by a Regional Detection Method.

Motivated by the fact that the danger may increase if the source of pollution problem remains unknown, in this paper, we study the source sensing problem for subdiffusion processes governed by time fractional diffusion systems based on a limited number of sensor measurements. For this, we first give some preliminary notions such as source, detection and regional spy sensors, etc. Secondly, we investigate the characterizations of regional strategic sensors and regional spy sensors. A regional detection approach on how to solve the source sensing problem of the considered system is then presented by using the Hilbert uniqueness method (HUM). This is to identify the unknown source only in a subregion of the whole domain, which is easier to be implemented and could save a lot of energy resources. Numerical examples are finally included to test our results