Analytical and qualitative investigation of COVID-19 mathematical model under fractional differential operator

Kamal Shah; Muhammad Sher; Hussam Rabai'ah; Ali Ahmadian; Soheil Salahshour; Bruno A Pansera

doi:10.1002/mma.7704

Analytical and qualitative investigation of COVID-19 mathematical model under fractional differential operator

Math Methods Appl Sci. 2021 Aug 22:10.1002/mma.7704. doi: 10.1002/mma.7704. Online ahead of print.

Authors

Kamal Shah¹, Muhammad Sher¹, Hussam Rabai'ah^{2

3}, Ali Ahmadian^{4

5}, Soheil Salahshour⁶, Bruno A Pansera⁷

Affiliations

¹ Department of Mathematics University of Malakand Chakdara Pakistan.
² College of Engineering Al Ain University Al Ain UAE.
³ Mathematics Department Tafila Technical University Tafila Jordan.
⁴ Institute of IR 4.0 The National University of Malaysia Bangi Malaysia.
⁵ Department of Mathematics Near East University Nicosia Turkey.
⁶ Faculty of Engineering and Natural Sciences Bahcesehir University Istanbul Turkey.
⁷ Department of Law Economics and Human Sciences, Mediterranea University of Reggio Calabria Reggio Calabria Italy.

Abstract

In the current article, we aim to study in detail a novel coronavirus (2019-nCoV or COVID-19) mathematical model for different aspects under Caputo fractional derivative. First, from analysis point of view, existence is necessary to be investigated for any applied problem. Therefore, we used fixed point theorem's due to Banach's and Schaefer's to establish some sufficient results regarding existence and uniqueness of the solution to the proposed model. On the other hand, stability is important in respect of approximate solution, so we have developed condition sufficient for the stability of Ulam-Hyers and their different types for the considered system. In addition, the model has also been considered for semianalytical solution via Laplace Adomian decomposition method (LADM). On Matlab, by taking some real data about Pakistan, we graph the obtained results. In the last of the manuscript, a detail discussion and brief conclusion are provided.

Keywords: Adomian decomposition method; analytical results; fractional‐order derivative; graphical interpretation; novel coronavirus mathematical models.