Approximating local solution of  IVPs of nonlinear first order ordinary hybrid integrodifferential equations:

Janhavi Dhage; Bapurao Dhage

doi:10.26637/mjm1104/002

Abstract

In this paper, we prove a couple of approximation results for local existence and uniqueness of the solution of a IVP of nonlinear first order ordinary hybrid integrodifferential equations by using the Dhage monotone iteration method based on a hybrid fixed point theorem of Dhage (2022) and Dhage {et al.} (2022). An approximation result for the Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established. Finally, our main abstract results are also illustrated with a couple of numerical examples.

Keywords:

Integrodifferential equation, Hybrid fixed point principle, Dhage Monotone iteration method, Ulam-Hyers stability, Nonlinear initial value problems, Hybrid differential equation, Dhage iteration method, Existence and approximation theorem

Mathematics Subject Classification:

34A12, 34A34

Authors Imprint References Funding Related Articles Downloads

Janhavi Dhage Kasubai, Gurukul Colony, Thodga Road, Ahmedpur - 413515, Dist. Latur, Maharashtra, India.
Bapurao Dhage Kasubai, Gurukul Colony, Thodga Road, Ahmedpur - 413515, Dist. Latur, Maharashtra, India. https://orcid.org/0000-0002-2353-8618

Pages: 344-355
Date Published: 01-10-2023
Vol. 11 No. 04 (2023): Malaya Journal of Matematik (MJM)

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