Extensive View for Implicit Second-Order Differential Equations with a Feedback Control

A. M. A.  El-Sayed; Sh. M. Al-Issa; H. H. G.  Hashem; I. H.  Kaddoura; M. E. A.  Jaafar

doi:10.37256/cm.6320256357

Authors

A. M. A. El-Sayed Department of Mathematics, Faculty of Sciences, Alexandria University, Alexandria, Egypt https://orcid.org/0000-0001-7092-7950
Sh. M. Al-Issa Department of Mathematics, Faculty of Arts and Sciences, Lebanese International University, Saida, Lebanon https://orcid.org/0000-0002-1488-0817
H. H. G. Hashem Department of Mathematics, Faculty of Sciences, Alexandria University, Alexandria, Egypt https://orcid.org/0000-0002-9921-832X
I. H. Kaddoura Department of Mathematics, Faculty of Arts and Sciences, Lebanese International University, Saida, Lebanon https://orcid.org/0000-0003-3627-6941
M. E. A. Jaafar Department of Mathematics, Faculty of Arts and Sciences, Lebanese International University, Saida, Lebanon

DOI:

https://doi.org/10.37256/cm.6320256357

Keywords:

existence results, Krasnoselskii's fixed point theorem, Ulam-Hyers stability, feedback control

Abstract

The current research investigates the solvability and stability of implicit second-order differential equations subject to fractional integral boundary conditions under the influence of a fractional control. The analysis is grounded in the application of Krasnoselskii’s fixed point theorem to establish the existence and stability of solutions. To complement the theoretical results, numerical calculations are provided, to validate our findings. Furthermore, detailed comparisons with the existing literature highlight the efficacy and novelty of the proposed approach.

Extensive View for Implicit Second-Order Differential Equations with a Feedback Control

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