Document Type
Original Study
Subject Areas
Mathematics
Keywords
Functional equations; existence of solutions; continuous dependence; state–dependence; self– reference.
Abstract
We present in this paper a new type of self-reference functional integro-differential equation with a nonlocal initial condition. Also, we present a nonlocal problem of the functional integro-differential equation with the infinite point boundary condition for more generalization. An integral representation equivalent to the functional integro-differential equation is obtained to use the theorems needed for proving the existence, and uniqueness. Then we prove the continuous dependence of the solution on the nonlocal parameter and the initial data of the equation. To prove the existence of the solution of the equation we present the Schauder fixed point theorem for both finite and infinite boundary conditions, and to prove that this solution is unique we use the Banach fixed point theorem. At last, we produce an example of a self-reference functional integro-differential equation with a nonlocal initial condition to discuss the solution of that equation.
How to Cite This Article
Darwish, A.A.; Seddeek, M.A.; Ahmed, Reda Gamal; El-Deeb, Ahmed A.; Mohamed, Moataz Ashraf; and Ghany, Hossam A.
(2024)
"Solvability of Self Reference Functional Integro-Differential Equation with Nonlocal Initial Condition,"
Trends in advanced sciences and technology: Vol. 1:
Iss.
1, Article 9.
DOI: 10.62537/2974-444X.1015
Available at:
https://tast.researchcommons.org/journal/vol1/iss1/9
