A Fractional-Order Sequential Hybrid System with an Application to a Biological System

Hasib Khan,Hashim M Alshehri,Zareen A Khan,Constantin Udriste

doi:10.1155/2021/2018307

Abstract

With the help of Banach’s fixed-point approach and the Leray–Schauder alternative theorem, we produced existence results for a general class of fractional differential equations in this paper. The proposed problem is more comprehensive and applicable to real-life situations. As an example of how our problem might be used, we have created a fractional-order COVID-19 model whose solution is guaranteed by our results. We employed a numerical approach to solve the COVID-19 model, and the results were compared for different fractional orders. Our numerical results for fractional orders follow the same pattern as the classical example of order 1, indicating that our numerical scheme is accurate.

Highlights

In science and engineering, fractional-order operators have lately been investigated for the modeling of dynamical systems. ere are operators based on singular kernels and nonsingular kernels
Atangana and Araz focused on the modeling and existence results of the COVID-19 model [1, 2]. e area of fractional calculus is still open for the researchers to investigate nonlinear models for their theoretical and computational studies with the help of [6,7,8,9]
In order to highlight the literature for the existence results and numerical simulations and their applications, we present some examples

Summary

Introduction

Fractional-order operators have lately been investigated for the modeling of dynamical systems. ere are operators based on singular kernels and nonsingular kernels. E area of fractional calculus is still open for the researchers to investigate nonlinear models for their theoretical and computational studies with the help of [6,7,8,9]. Tuan et al [5] gave some theoretical and computational studies of a fractional-order COVID-19 model for the existence and numerical simulations by the help of Haar wavelets approach. To the best of our knowledge, existence, uniqueness, and stability results had never been studied for BVP (1) Such situation may have importance in application point of view and in theoretical development and can be studied in the work of Dhage in [12,13,14] and the reference therein

Existence Criteria

Hyers–Ulam Stability

Application

Computational Results

Conclusion