New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control

Abstract

The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is 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+). Also, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions to that multidimensional functional equation. Additionally, we give an example and some particular cases to illustrate our outcomes.

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.…”