A constrained problem of a nonlinear functional integral equation subject to the pantograph problem
Elghanam, E., El-Sayed, A., Elalem, M. (2023). A constrained problem of a nonlinear functional integral equation subject to the pantograph problem. EKB Journal Management System, 1(2), 80-83. doi: 10.21608/ajst.2024.257068.1023
Esraa Samy Elghanam; Ahmed M. A. El-Sayed; Mahmoud Elalem. "A constrained problem of a nonlinear functional integral equation subject to the pantograph problem". EKB Journal Management System, 1, 2, 2023, 80-83. doi: 10.21608/ajst.2024.257068.1023
Elghanam, E., El-Sayed, A., Elalem, M. (2023). 'A constrained problem of a nonlinear functional integral equation subject to the pantograph problem', EKB Journal Management System, 1(2), pp. 80-83. doi: 10.21608/ajst.2024.257068.1023
Elghanam, E., El-Sayed, A., Elalem, M. A constrained problem of a nonlinear functional integral equation subject to the pantograph problem. EKB Journal Management System, 2023; 1(2): 80-83. doi: 10.21608/ajst.2024.257068.1023

A constrained problem of a nonlinear functional integral equation subject to the pantograph problem

Alexandria Journal of Science and Technology
Volume 1, Issue 2, December 2023, Page 80-83  XML PDF (385.97 K)
Document Type: Original Article
DOI: 10.21608/ajst.2024.257068.1023
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Authors
Esraa Samy Elghanam email 1; Ahmed M. A. El-Sayed2; Mahmoud Elalem3
1Department of Mathematics,Faculty of science,Alexandria university,Alexandria,Egypt.
2Mathematics and computer science department, Faculty of Science, Alexandria University, Egypt
3Department of mathematics,Faculty of science,Alexandria university,Alexandria,Egypt.
Abstract
Here we study the existence of solution and its continuous dependence of a constrained problem of a nonlinear functional integral equation subject to the constraint of the initial value problem of the pantograph differential equation. The Hyers-Ulam stability of the problem will be proved.
Here we study the existence of a unique solution y ϵ C[0,T] of (1) where the function u is the solution of the initial value problem of the pantograph equation
du/dt=f2 (t,u(t),u(ɤt)), a.e. t ϵ (0,T] and u(0)=u0 . (2)
Here, we prove the existence of a unique solution u ϵ C [0, T] of the problem (2) and study the continuous dependence of the solution u on ɤ and u_0.
Secondly, we prove the existence of a unique solution of the integral equation (1) and study the continuous dependence of y on u, β, λ.
Finally, we study Hyers-Ulam stability of our problem (1) , (2).
Keywords
continuous dependence; existence of solution; Hyers-ulam stability
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