This paper describes a new fractional predator–prey discrete system of the Leslie type. In addition, the non-linear dynamics of the suggested model are examined within the framework of commensurate and non-commensurate orders, using different numerical techniques such as Lyapunov exponent, phase portraits, and bifurcation diagrams. These behaviours imply that the fractional predator–prey discrete system of Leslie type has rich and complex dynamical properties that are influenced by commensurate and incommensurate orders. Moreover, the sample entropy test is carried out to measure the complexity and validate the presence of chaos. Finally, nonlinear controllers are illustrated to stabilize and synchronize the proposed model.
Owing to the COVID-19 pandemic, which broke out in December 2019 and is still disrupting human life across the world, attention has been recently focused on the study of epidemic mathematical models able to describe the spread of the disease. The number of people who have received vaccinations is a new state variable in the COVID-19 model that this paper introduces to further the discussion of the subject. The study demonstrates that the proposed compartment model, which is described by differential equations of integer order, has two fixed points, a disease-free fixed point and an endemic fixed point. The global stability of the disease-free fixed point is guaranteed by a new theorem that is proven. This implies the disappearance of the pandemic, provided that an inequality involving the vaccination rate is satisfied. Finally, simulation results are carried out, with the aim of highlighting the usefulness of the conceived COVID-19 compartment model.
Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the SEIR model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings.
Neurodegenerative diseases drastically affect human beings without distinction; it does not matter if they are male or female. Sometimes, it is not clear why a person in their life developed a well-known disease in the world such as Parkinson’s disease (PD). Nowadays, various novel machine learning-based algorithms for evaluating Parkinson’s disease have been designed. The most recent strategy, which was developed using deep learning and can forecast the severity of Parkinson’s disease, is the one described here. To identify this disease, a thorough medical history, previous treatment history, physical examinations, and some blood tests and brain films must be completed. Diagnoses are more critical since they are less expensive and less time-consuming. Voice data from 253 people used in the current study corroborates the doctor’s diagnosis of Parkinson’s disease. To acquire the best results from the data, preprocessing is done. To perform the balancing procedure, a systematic sampling strategy was used to select the data that would be analyzed. Several data groups were constructed using a feature selection technique based on the label’s effect strength. Classification algorithms and performance evaluation criteria employ DT, SVM, and kNN. The classification algorithm and data group with the highest performance value were chosen, and the model was created due to this selection. The SVM approach was employed when constructing the model, and 45% of the original data set data were used. The data was sorted from most relevant to least important. 86% performance accuracy was achieved, in addition to excellent results in all other areas of the project. As a result, it has been established that medical decision support will be provided to the doctor with the assistance of the data set obtained from the speech recordings of the individual who may have Parkinson’s disease and the model that has been developed.
This paper proves several new inequalities for the Euclidean operator radius, which refine some recent results. It is shown that the new results are much more accurate than the related, recently published results. Moreover, inequalities for both symmetric and non-symmetric Hilbert space operators are studied.
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