Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis

Abstract

In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in BC(R+). In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions.

An Outlook on Hybrid Fractional Modeling of a Heat Controller with Multi-Valued Feedback Control

“…The use of various approaches for certain differential and integral problems, including constraints or control variables, has recently been developed by several scholars, for example, in refs. [27][28][29][30][31][32][33]. This feedback control may be in an implicit form as in [27][28][29][30], multi-valued feedback control as in [32], or fractal feedback control [33].…”

“…[27][28][29][30][31][32][33]. This feedback control may be in an implicit form as in [27][28][29][30], multi-valued feedback control as in [32], or fractal feedback control [33].…”

An outlook on stability of implicit θ -Caputo fractional differential equation with application involving the Riemann-Stieltjes type

“…Fractional calculus is a potent tool in applied mathematics, offering a way to analyze a wide range of problems in various scientific and technical fields. Fractional derivatives have yielded significant results in [5,[18][19][20][21][22][23]. The study of partial fractional differential equations, as well as ordinary differential equations, has made substantial progress in recent years.…”

Solvability of an Initial-value Problem of Non-linear Implicit Fractal Differential Equation

“…They are characterized by their non-linearity and often exhibit complex behaviours, such as chaos and self-replication (see [13,14]). Differential equations and fractal differential equations have applications in various fields, including physics, biology, and finance, and have garnered significant interest due to their ability to model complex systems with remarkable precision (see [1,4,6,10,12]). In this paper we will focus on this initial-value problem of nonlinear implicit fractal differential equation.…”