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In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the general fractional derivative to analyze the impact. The Laplace decomposition technique is employed to obtain the numerical outcomes of the model. In order to observe the effect of the diffusion component in the SIR model, graphical solutions are also displayed. [ABSTRACT FROM AUTHOR]

Numerous novel concepts in fractional mathematics have been created to provide numerical models for a variety of real-world, engineering, and scientific challenges because of the kernel’s memory and non-local effects. In this post, we have looked at a deadly illness known as rabies. For our analysis, we employed the Atangana–Baleanu fractional derivative in Caputo sense. Additionally, the mathematical answer was obtained by applying the Laplace transform. Our approach is distinct, and we illustrated the vital role immunizations play in limiting the spread of the illness using graphical data. Furthermore, in this article, we have shown that fractional order systems are preferable to integer order systems. [ABSTRACT FROM AUTHOR]

The whole world is suffering from a pandemic virus known as COVID-19 nowadays. This virus is also known as novel corona virus. There are various statements coming out regarding its generation but till now one thing is coming is that its origin place seems to be a lab somewhere in Wuhan city of China. It is also said off and on the record that covid-19 virus came into existence near November 2019 but on record, the WHO office (China) reported on 31st December 2019 that an unknown virus is detected in Wuhan city. On 7th January 2020, Chinese authorities announced about the existence of this virus. At the initial stage, it was supposed that this virus might be bat-origin but after that several other statements are coming day by day. Authors are not going to discuss about the causes of its origin. But since this virus has become the pandemic around the world so it is necessary to study this virus and its nature to predict the future outbreaks and also control strategies by using mathematical modeling. In this paper, we are going to study the model by using Atangana-Baleanu fractional operator. Also we calculated the numeric results with graphical representation. [ABSTRACT FROM AUTHOR]

In this article, we investigate the solution of the fractional multidimensional Navier–Stokes equation based on the Caputo fractional derivative operator. The behavior of the solution regarding the Navier–Stokes equation system using the Sumudu transform approach is discussed analytically and further discussed graphically. [ABSTRACT FROM AUTHOR]

Cancer is a fatal disease for a very long time. It has its own history. Now it has become one of the major reasons for death due to its various types. Researchers, scientists and doctors are trying to find out the success and minimize the death rate in this field. The fact is, cancer treatment is only effective when it has been diagnosed at a very early stage. Therefore, cancer is a kind of provocative topic for analysis. In this paper, we have shown the growth of cancer cells, normal cells along with chemotherapeutic cells. We have shown that the effect of chemotherapeutic drugs is highest at the centre of tumour affected area. We have used the Yang–Abdel–Cattani fractional operator with Laplace transform for all numeric calculations. Apart from numerical calculations, we have also shown the graphical representation of cell growth. [ABSTRACT FROM AUTHOR]

Many years have passed since the model that outlined the connection between sugar and insulin was developed, and a great deal of study and investigation has subsequently been done on it. In this work, we investigated the disparities in the Modified Bergman’s glucose–insulin model between Yang–Abdel–Cattani derivative and Caputo–Fabrizio derivative. With our improvements, the prior model now includes the diet, which is a crucial component of the blood glucose model. Based on results, the new model outperforms the previous one in terms of accuracy. To highlight the significance of fractional derivatives, we also established the fractional models. In addition, we verified the existence and uniqueness of the results and offered a graphical and numerical depiction of the findings. [ABSTRACT FROM AUTHOR]