Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives

Vedat Suat Erturk; Pushpendra Kumar

doi:10.1016/j.chaos.2020.110280

Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives

Chaos Solitons Fractals. 2020 Oct:139:110280. doi: 10.1016/j.chaos.2020.110280. Epub 2020 Sep 21.

Authors

Vedat Suat Erturk¹, Pushpendra Kumar²

Affiliations

¹ Department of Mathematics, Ondokuz Mayis University, Atakum Samsun, 55200, Turkey.
² Department of Mathematics and Statistics, School of Basic and Applied Sciences,Central University of Punjab, Bathinda, Punjab 151001, India.

Abstract

In this manuscript, we solve a model of the novel coronavirus (COVID-19) epidemic by using Corrector-predictor scheme. For the considered system exemplifying the model of COVID-19, the solution is established within the frame of the new generalized Caputo type fractional derivative. The existence and uniqueness analysis of the given initial value problem are established by the help of some important fixed point theorems like Schauder's second and Weissinger's theorems. Arzela-Ascoli theorem and property of equicontinuity are also used to prove the existence of unique solution. A new analysis with the considered epidemic COVID-19 model is effectuated. Obtained results are described using figures which show the behaviour of the classes of projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of non-linear equations. The present study can confirm the applicability of the new generalized Caputo type fractional operator to mathematical epidemiology or real-world problems. The stability analysis of the projected scheme is given by the help of some important lemma or results.

Keywords: 26A33; 34C60; 92C60; 92D30; COVID-19; Fixed point theorems; Mathematical model; New generalized Caputo-type fractional derivative; Predictor-corrector algorithm.