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Novel coronavirus (COVID‐19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID‐19 SEIR epidemic model via Caputo fractional derivatives using a predictor–corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag–Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs. [ABSTRACT FROM AUTHOR]

New atypical pneumonia caused by a virus called Coronavirus (COVID-19) appeared in Wuhan, China in December 2019. Unlike previous epidemics due to the severe acute respiratory syndrome (SARS) and the Middle East respiratory syndrome coronavirus (MERS-CoV), COVID-19 has the particularity that it is more contagious than the other previous ones. In this paper, we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29, 2020 with the uses of fractional derivatives, namely, Caputo derivatives, the Caputo–Fabrizio derivatives, and Atangana–Baleanu derivatives in the Caputo sense. The fixed point theory and Picard–Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investigations. For each fractional model, we propose a numerical scheme as well as prove its stability. Using parameter values estimated from the Japan COVID-19 epidemic real data, we perform numerical simulations to confirm the effectiveness of used approximation methods by numerical simulations for different values of the fractional-order γ , and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals. [ABSTRACT FROM AUTHOR]

The first symptomatic infected individuals of coronavirus (Covid‐19) was confirmed in December 2020 in the city of Wuhan, China. In India, the first reported case of Covid‐19 was confirmed on 30 January 2020. Today, coronavirus has been spread out all over the world. In this manuscript, we studied the coronavirus epidemic model with a true data of India by using Predictor‐Corrector scheme. For the proposed model of Covid‐19, the numerical and graphical simulations are performed in a framework of the new generalised Caputo sense non‐integer order derivative. We analysed the existence and uniqueness of solution of the given fractional model by the definition of Chebyshev norm, Banach space, Schauder's second fixed point theorem, Arzel's‐Ascoli theorem, uniform boundedness, equicontinuity and Weissinger's fixed point theorem. A new analysis of the given model with the true data is given to analyse the dynamics of the model in fractional sense. Graphical simulations show the structure of the given classes of the non‐linear model with respect to the time variable. We investigated that the mentioned method is copiously strong and smooth to implement on the systems of non‐linear fractional differential equation systems. The stability results for the projected algorithm is also performed with the applications of some important lemmas. The present study gives the applicability of this new generalised version of Caputo type non‐integer operator in mathematical epidemiology. We compared that the fractional order results are more credible to the integer order results. [ABSTRACT FROM AUTHOR]