Existence and approximation for nonlinear dynamic equations using monotone iteration method

Nour Alsharif

Existence and approximation for nonlinear dynamic equations using monotone iteration method

Abstract

This paper improves a generalized monotone iterative technique for solving dynamic initial value problems (IVPs) on time scales, using the method of coupled lower and upper solutions. We construct monotone sequences of iterates, each of which corresponds to a solution of the dynamic IVP on time scales. Under suitable conditions, we establish the uniform and monotonic convergence of sequences to the extremal (minimal and maximal) solutions of the problem. The results provide a unified framework for analyzing dynamic equations on time scales via monotone iteration.

Keywords

References

Bhaskar TG, McRae FA. Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions. Appl Math Comput. 2002; 133(1): 187-92.
Bohner M, Peterson A. Advances in dynamic equations on time scales. Boston, MA, Birkhäuser; 2003.
Denton Z, Vatsala AS. Monotone iterative technique for finite systems of nonlinear Riemann-Liouville fractional differential equations. Opuscula Math. 2011; 31(3): 327-39.
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Kaymakçalan B. Monotone iterative method for dynamic systems on time scales. Dynam Systems Appl. 1993;2(2):213-20.
Ladde GS, Lakshmikantham V, Vatsala AS. Monotone iterative techniques for nonlinear differential equations. London: Pitman; 1985.
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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Nour Alsharif ^*
0009-0008-5793-5946
Türkiye

Publication Date

July 31, 2025

Submission Date

April 15, 2025

Acceptance Date

June 2, 2025

Published in Issue

Year 2025 Volume: 2 Number: 2

IZ

https://izlik.org/JA84RT82WF

Cite

RIS / Bibtex

APA

Alsharif, N. (2025). Existence and approximation for nonlinear dynamic equations using monotone iteration method. Hitit Journal Of Science, 2(2), 31-36. https://izlik.org/JA84RT82WF

AMA

1.Alsharif N. Existence and approximation for nonlinear dynamic equations using monotone iteration method. HJS. 2025;2(2):31-36. https://izlik.org/JA84RT82WF

Chicago

Alsharif, Nour. 2025. “Existence and Approximation for Nonlinear Dynamic Equations Using Monotone Iteration Method”. Hitit Journal Of Science 2 (2): 31-36. https://izlik.org/JA84RT82WF.

EndNote

Alsharif N (July 1, 2025) Existence and approximation for nonlinear dynamic equations using monotone iteration method. Hitit Journal Of Science 2 2 31–36.

IEEE

[1]N. Alsharif, “Existence and approximation for nonlinear dynamic equations using monotone iteration method”, HJS, vol. 2, no. 2, pp. 31–36, July 2025, [Online]. Available: https://izlik.org/JA84RT82WF

ISNAD

Alsharif, Nour. “Existence and Approximation for Nonlinear Dynamic Equations Using Monotone Iteration Method”. Hitit Journal Of Science 2/2 (July 1, 2025): 31-36. https://izlik.org/JA84RT82WF.

JAMA

1.Alsharif N. Existence and approximation for nonlinear dynamic equations using monotone iteration method. HJS. 2025;2:31–36.

MLA

Alsharif, Nour. “Existence and Approximation for Nonlinear Dynamic Equations Using Monotone Iteration Method”. Hitit Journal Of Science, vol. 2, no. 2, July 2025, pp. 31-36, https://izlik.org/JA84RT82WF.

Vancouver

1.Nour Alsharif. Existence and approximation for nonlinear dynamic equations using monotone iteration method. HJS [Internet]. 2025 Jul. 1;2(2):31-6. Available from: https://izlik.org/JA84RT82WF