2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

A new study of unreported cases of 2019-nCOV epidemic outbreaks

Preface: graph colorings

A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R0≈6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease. 

A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects

A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R 0 ≈ 6.6361 . Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.

We investigate the existence of solutions for a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions. In this way, we use a generalization of the hybrid Dhage’s fixed point result for sum of three fractional operators. Finally, we give an example to illustrate our main result.

On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators

In this article, the controllability results of the non-dense Hilfer neutral fractional derivative (HNFD) are presented. The results are acknowledged using semigroup theory, fractional calculus, Banach contraction principle, and Monch technique. Moreover, a numerical analysis is given to enhance our model.

An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain

This study reveals the fractional integrodifferential equation with nondense nature in the Banach space. We acknowledge the existence of a control term by the Monch fixed point theorem and noncompact measure. An illustration is offered to validate our analytical results.

New results on controllability in the framework of fractional integrodifferential equations with nondense domain

This work establishes the controllability of nondense fractional neutral delay differential equation under Hille-Yosida condition in Banach space. The outcomes are derived with the aid of fractional calculus theory, semigroup operator theory and Schauder fixed point theorem. Theoretical results are verified through illustration.

https://www.aimsciences.org/article/exportPdf?id=2e83661d-5799-47a1-ac9b-1d168ba1f5c3

Results on controllability of non-densely characterized neutral fractional delay differential system

This article investigates the issue of optimal control and approximate controllability results for fractional integrodifferential evolution equations with infinite delay of r∈(1,2) in Banach space. In the beginning, we analyze approximate controllability results for fractional integrodifferential evolution equations using the fractional calculations, cosine families, and Banach fixed point theorem. After, we developed the continuous dependence of the fractional integrodifferential evolution equations by using the Henry–Gronwall inequality. Furthermore, we tested the existence of optimal controls for the Lagrange problem. Lastly, an application is presented to illustrate the theory of the main results.

K. Kaliraj

Papers

An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain

New results on controllability in the framework of fractional integrodifferential equations with nondense domain

Results on controllability of non-densely characterized neutral fractional delay differential system

Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order r∈(1,2)

Controllability analysis for impulsive integro-differential equation via Atangana–Baleanu fractional derivative