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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan
Jalina Widjaja
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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On Conditions for Controllability and Local Regularity of A System of Differential Equations Ahmad Hadra Zuhri; Yudi Soeharyadi; Jalina Widjaja
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 2 (JULY 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.2.1584.259-270

Abstract

We consider a system of differential equations on a Banach space X given by: x'(t) = Ax(t) + u(t)f(t, x(t)), x(0) = x0, where A is an infinitesimal generator of a C0-semigroup, f : R0+ × X → X is a locally Lipschitz function, and u ∈ Lp([0, T], R) is a control defined on [0, T] with 1 < p ≤ ∞. Using the Compactness Principle and the generalization of Gronwalls Lemma, the system is shown to be controllable for a γ-bounded function f. Another result of this study is the local existence and the uniqueness of the solution of the system for locally bounded function f through weighted ω-norm.
A MODEL ON MARKET EQUILIBRIUM USING A DIFFERENTIAL EQUATION WITH TIME DELAYS Widjaja, Jalina; Putra Irawan, Naufal Zidan; Soeharyadi, Yudi; Tampubolon, Dumaria R.
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1893-1904

Abstract

In this paper, a model on market equilibrium is proposed using a delay differential equation with discrete delays as a modified version of the one proposed by Kobayashi (1996). The price of a commodity is determined using the equation involving weighted supply and demand functions. Both supply and demand functions are considered at the current time and sometimes in the past. The delays are chosen by considering the seasonal behavior of the market. We use data on some main commodities in Indonesia from 2018 to 2024 to validate the model. We found that the implementation of our modified Kobayashi model improves the estimation given by the original one. The implementation of the method also shows some characteristics of delay equations, that is longer delay time may include more dynamics, and more fluctuation, although that means it is more prone to instabilities. However, the problem of optimal delay time is yet to be resolved.
Co-Authors Ahmad Hadra Zuhri Dumaria R. Tampubolon Putra Irawan, Naufal Zidan Yudi Soeharyadi Yudi Soeharyadi