Stability of Perturbed Set Differential Equations Involving Causal Operators in Regard to Their Unperturbed Ones considering Difference in Initial Conditions

Abstract

We investigate the stability of solutions of perturbed set differential equations with causal operators in regard to their corresponding unperturbed ones considering the difference in initial conditions (time and position) by utilizing Lyapunov functions and Lyapunov functionals.

Application of exponential tight differential operators to the solution of the infectious disease equation

“…To solve this problem, relevant personnel designed a high-precision compact difference scheme to numerically solve the infectious disease equation. We can use the Finite Difference Method, and then discretize the equation [11]. First, we design a simple infectious disease model, namely SIR model, which is mainly used to describe the dynamic balance [12] among the susceptible, infected and recovered groups.…”

The Stability of Set-Valued Differential Equations with Different Initial Time in the Sense of Fractional-like Hukuhara Derivatives

“…Up till now, there are some results of fractional differential equations in this case, we can find it in [26][27][28][29]. there are few studies of set-valued differential equations with different initial time in the sense of fractional-like Hukuhara derivatives (see [30]).…”

Lagrange stability in terms of two measures with initial time difference for set differential equations involving causal operators

“…Many researchers were interested in studying set differential equations (SDEs) in the recent decades [2,3,5,[8][9][10]13,14,18,20,23,36,47] due to their unifying properties. Lakshmikantham et al highlighted these properties in one of the most important resources on this topic [23].…”

“…[1, 7-10, 21, 43] SDEs with causal operators unifies the fundamental theory of SDEs, including various corresponding dynamical systems. Some relevant works can be found in [5,[8][9][10][11][12][13][14]47] Although it is never feasible to know the exact solutions of all dynamical systems in practice, their attributes may be determined through a variety of qualitative studies such as stability analysis [2][3][4][5]15,19,20,24,36], initial time difference (ITD) stability analysis [6,29,30,33,34,37,38,[41][42][43][44][45][46][47], practical stability analysis [17,31,40,46], boundedness [2,6,11,16,32,37,38,[40][41][42], etc.…”