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

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.

Existence and stability analysis to the sequential coupled hybrid system of fractional differential equations with two different fractional derivatives

“…Even if there are no unfavourable factors, very few inaccuracies in the initial population count (c) or breeding rate (a) will result in fairly significant errors in prediction. One of the interesting subjects in this area, is the investigation of the existence and stability of solutions, because the study of the existence of solution of the fractional differential equation(FDE) became important due to the lack of a general formula for solving nonlinear FDEs, see [29,30,32,33]. Recently, Some scholars have discussed the existence, uniqueness, and different types of Ulam stability of solutions of fractional sequential hybrid differential equations [29,32,33] and the references cited therein.…”

“…One of the interesting subjects in this area, is the investigation of the existence and stability of solutions, because the study of the existence of solution of the fractional differential equation(FDE) became important due to the lack of a general formula for solving nonlinear FDEs, see [29,30,32,33]. Recently, Some scholars have discussed the existence, uniqueness, and different types of Ulam stability of solutions of fractional sequential hybrid differential equations [29,32,33] and the references cited therein. The classical form of hybrid differential equation [35] is given by the following differential equation…”

“…Hybrid differential equations and coupled hybrid systems involving fractional derivatives have also been investigated by scientific researchers; see for instance [22][23][24][25][26][27][28] and the references cited therein. In recent years, sequential fractional hybrid differential equations have been studied by several researchers [29][30][31][32][33][34]. On the other hand, the stability of solutions of differential equations is important in physical problems because if slight deviations from the mathematical model caused by unavoidable errors in measurement do not have a correspondingly slight effect on the solution, the mathematical equations describing the problem will not accurately predict the future outcome.…”

Analysis and Investigation of Trilateral Spinning Based on the Concentric Circle Trajectory

“…The simulation was performed in ABAQUS 2016/Explicit software. To shorten the duration of the simulation experiment without affecting the results, we employed the technique of equivalent transformation [25][26][27]. The motion of the rollers rotated around the roller principal axis to process the workpiece, which rotated itself, was set as the workpiece static, the roller principal axis revolved around the workpiece, while the rollers revolved around the roller principal axis.…”

Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function

“…For example, using the Saigo fractional integral operators, Khan et al [7] presented some inequalities for a class of n-decreasing positive functions. With the help of fixedpoint theorems and inequalities analysis techniques, Baleanu et al [8] and Khan et al [9] investigated the existence results for hybrid fractional differential equation boundary value problems, respectively. At present, there have been a great deal of fractional integral operators and their applications introduced in the books [10,11].…”