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, Pages 80-83 PDF (385.97 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/ajst.2024.257068.1023 | ||
| Authors | ||
| Esraa Samy Elghanam* 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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