DOI: 10.12732/ijam.v37i1.1
RESULTS ON EXISTENCE AND
UNIQUENESS OF SOLUTIONS OF
DYNAMIC EQUATIONS ON TIME
SCALE VIA GENERALIZED
ORDINARY DIFFERENTIAL
EQUATIONS
Igobi Dodi Kanu 1,§ , Michael Precious Ineh
1 Department of Mathematics,University of Uyo
P.M.B. 1017, NIGERIA
2 Ritman University Ikot-Ekpene, NIGERIA
Abstract. The non-absolutely convergent integral of some functions of dynamic equations
failed the requirement of the derivative of the function existing everywhere, and so the loss uniqueness of the indefinite integral is the setback in the theory of timescale calculus. In this work, we addressed this challenge in the context of the generalized ordinary differential equation. The well-established relationship between the dynamic equations on time-scale and the generalized ordinary differential equations is used to develop theorems and proofs on the
existence and uniqueness of solutions of the dynamic equations on time-scale. The notion is demonstrated with examples and the outcomes obtained validate the concept’s applicability.
How
to cite this paper?
DOI: 10.12732/ijam.v37i1.1
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 1
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