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Jurnal Diferensial
Published by Universitas Nusa Cendana
ISSN : -     EISSN : 27759644     DOI : -
Core Subject : Economy, Health, Science, Education,
Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Public Health
Jurnal Diferensial adalah jurnal sains yang bertujuan untuk menyebarluaskan hasil riset-riset ataupun kajian pustaka pada bidang ilmu matematika dan terapannya. Artikel-artikel pada jurnal ini difokuskan kepada bidang ilmu matematika dan terapannya. Ruang lingkup atau bidang ilmu yang diterima dijurnal ini (tetapi tidak terbatas pada) adalah Analisis, Aljabar, Teori Graf, Optimisasi, Riset Operasi, Statistik, Biomatematika.
Arjuna Subject : Matematika - Matematika Terapan
Articles 90 Documents
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Modelling Immunological Effects on Fractional Order of Cholera Dynamics with Behavioral Response via Numerical simulation Kolawole, Mutairu Kayode; Adeniji, Atinuke Abidemi
JURNAL DIFERENSIAL Vol 7 No 2 (2025): November 2025
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v7i2.23609

Abstract

Cholera, spread by the bacterium Vibrio cholerae, is still a major health problem in places with unsanitary conditions. The way it spreads relies on the host’s immunity, certain environmental aspects and how clean people keep themselves and their properties. The model in this study applies Caputo fractional-order derivatives to capture the immunity of people, their hygiene, memory in diseases and various ways of controlling them. It includes the study of how people respond and interact with their environment and disease-related factors in a mathematical way. We perform solid analyses on the model, confirming the existence, uniqueness, positivity and boundedness of its solutions. A basic reproduction number is calculated to find out if the disease will continue to exist in a population. Analyzing what makes a disease-free state or an endemic equilibrium stable tells us how to best control the disease. Using the Laplace-Adomian Decomposition Method for solving the nonlinear fractional system results in simulations that match actual cholera behavior. Findings point out that a decline in immunity and better hygiene help reduce how cholera spreads. The framework supports an understanding of cholera spread and is also useful for examining other diseases that are highly complex.
Evaluasi Kinerja Uji Normalitas pada Ragam Distribusi dan Ukuran Sampel Wara, Shindi Shella May; Adziima, Andri Fauzan; Nasrudin, Muhammad; Pratama, Alfan Rizaldy
JURNAL DIFERENSIAL Vol 7 No 2 (2025): November 2025
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v7i2.24042

Abstract

The normal distribution is a fundamental assumption in many parametric statistical methods. Therefore, testing for data normality is a crucial step prior to further analysis. This study aims to evaluate the performance of three widely used normality test methods: Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and Shapiro-Wilk (SW), across various distributions (standard normal, exponential, and t-student with degrees of freedom 1, 20, and 100) and sample sizes (n = 20, 50, 100, 200, and 500). Data were generated through simulation with 1000 iterations for each combination. The results show that the KS method performs well on standard normal and t-student distributions with larger degrees of freedom. The AD method proves to be more sensitive, especially in detecting deviations from normality, though it is less stable for small sample sizes. Meanwhile, the SW method demonstrates optimal performance with large samples. These findings provide practical guidance in selecting appropriate normality test methods based on the characteristics of the data.
Nonlocal Metric Dimension of Windmill Graph Lathifah, Fithri Annisatun
JURNAL DIFERENSIAL Vol 7 No 2 (2025): November 2025
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v7i2.24460

Abstract

Let G = (V (G), E(G)) be a simple and connected graph. The distance between two vertices u and vin G, is the length of a shortest path from u to v, denoted by d(u, v). Suppose S = {s1, s2, ...sk} is anordered subset of vertices of G, then the metric representation of a vertex u ∈ V (G) with respect to S,denoted by r(u|S), is the k−vector (d(u, s1), d(u, s2), ..., d(u, sk)). If every two nonadjacent vertices ofG have distinct metric representations with respect to S, then the set S is called a nonlocal resolvingset for G. A nonlocal resolving set with minimum cardinality is called a nonlocal metric basis. Thenonlocal metric dimension of G is the cardinality of the nonlocal metric basis of G and is denoted bynldim(G). In this paper, we obtained nonlocal metric dimension of windmill graph.
Implementasi Fuzzy Mamdani pada Sistem Pendukung Keputusan Pemilihan Mobil Listrik Parwitasari, Ikha Puspita; Setyawan, Azis Putra
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.25024

Abstract

The rapid development of electric vehicles (EVs) has led to a wide variety of models with different specifications and prices, requiring a method that can evaluate multiple criteria simultaneously. This study applies the Mamdani fuzzy inference system to assess the suitability of EVs based on six key variables: price, production year, driving range, passenger capacity, power, and battery capacity. Triangular membership functions are used to represent the linguistic variables, and the rule base reflects realistic decision preferences. Through fuzzification, Mamdani inference, aggregation, and defuzzification, crisp suitability scores are produced for each vehicle. Results show that EVs with high specifications and proportional prices achieve the highest scores, while those with high prices but low specifications rank lowest. The fuzzy Mamdani approach effectively integrates linguistic and subjective criteria to support structured decision-making in EV selection.
A Solutions of the Linearized Two-Dimensional Generalized Dispersive Wave Equation with Mixed Derivative via the Residual Power Series Method Ali, Nawzad Hasan
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.26631

Abstract

This article applies the Residual Power Series Method (RPSM) to solve the Linearized Two-Dimensional Generalized Dispersive Wave Equation (L-2DGDWE) featuring the mixed derivative term $u_{xt}$. The RPSM is based on the general Taylor series formula combined with a residual error function minimization. A new analytical solution is investigated in this work. The analytical solution is designed to find approximate solutions via RPSM, and these obtained results are compared with exact solutions to demonstrate the precision, reliability, and rapid convergence of the proposed method. Graphical representations at different time instances are provided to visualize the solution behavior.
An Analysis of the COVID-19 Agenda Using Big Data from Social Media: A Comparative Study across Countries with R Programming İşleyen, Şakir; Zebari, Amar Yahya; Jameel, Hasan Hazim
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.26853

Abstract

Social media platforms are becoming increasingly important as sources of public discourse and real-time data analysis, as the COVID-19 epidemic has highlighted. Using the hashtag #COVID19, this study examines COVID-19-related tweets from seven nations (the US, Germany, South Korea, Iraq, Spain, Italy, and Turkey) in order to find trends in engagement and correlations. Similarities between public attitude and government communications are examined by statistical techniques such as content analysis, frequency analysis, and cross-delay correlation, as well as R programming. The findings show that tweet patterns from different countries are highly correlated, and that the Iraqi government's tweets with a typical theme were more popular than those with a COVID-19 theme. This study provides information on cross-border communication tactics in times of crisis and illustrates the potential of big data analytics for comprehending global phenomena.
Analysing Cholera-Measles Epidemics of a Fractional-Order Model with Preventive Strategies Using Laplace Adomian Decomposition Method Olaosebikan, Mutiu Lawal; Oladapo, Asimiyu Olalekan; Ogunniran, Muideen Odunayo
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.24154

Abstract

This study provides an in-depth examination of cholera-measles epidemics through a fractional-order mathematical model that integrates essential preventive measures. By employing fractional calculus, the model captures the memory and hereditary properties of disease transmission dynamics, offering a more realistic representation than classical integer-order models. This consists of multiple compartments representing the progression of each disease, with control measures such as treatment, vaccination, water sanitation and public health awareness integrated into the system. Considering numerical iteration on model to see how these changes affect the spread of disease. The results reveal that fractional-order models not only enhance the accuracy of epidemic forecasting but also demonstrate the effectiveness of timely and combined preventive strategies in reducing infection rates. Sensitivity analysis further identifies crucial parameters influencing disease dynamics, guiding resource allocation for optimal control. The findings indicate the relevance of fractional modeling and provides valuable insights for informing strategic planning efforts to curb cholera-measles transmission.
Perturbed Akbari-Ganji Method for the Solution of Singular Multi-Order Fractional Differential Equations Adebisi, Ajimot Folasade; Oseni, Wasiu Adewale
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.20714

Abstract

Differential equations, which involve derivatives, are fundamental in describing various physical and engineering phenomena. Newton’s second law of motion provides a basic example, which illustrates how force, mass, and acceleration relate through differential equations. These equations are widely used in science and engineering to model real-world systems. Fractional differential equations extend this concept by incorporating non-integer derivatives, allowing for a more generalized approach to complex problems. Multi-order fractional equations involve multiple fractional derivatives, while singular fractional equations contain terms that become undefined at specific points. We aim to explore the significance of fractional and singular fractional differential equations in mathematical modeling, highlighting their applications in capturing intricate behaviors across different fields and our results emphasize the broader applicability of these equations in solving advanced problems in physics, engineering, and applied sciences.
Mathematical Analysis and Control of Typhoid Fever Dynamics Using a SEITRB Fractional Model Kolawole, Mutairu Kayode; Ayoola, Rasheed Gbemisola; Oyalade, Abidemi Damaris; Ogunleye, Timothy A.; Ayoola, Adijat Omolara
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.24943

Abstract

The seitrb compartmental model was formulated to investigate the transmission dynamics and control of typhoid fever, incorporating the susceptible, exposed, infected, treatment, recovered, and environmental bacteria populations. The model was analyzed for well-posedness, establishing existence, uniqueness, positivity, and boundedness of solutions. Equilibrium states were examined under both disease-free and endemic conditions, with the basic reproduction number derived as the threshold parameter. The analysis showed that typhoid infection dies out when but persists when . Local and global stability analyses were established, while sensitivity analysis identified treatment rate, bacterial decay, and vaccination efficacy as the most influential parameters on . Numerical simulations, carried out using the Laplace Adomian Decomposition Method in conjunction with Caputo fractional derivatives, illustrated the impact of control measures. Findings revealed that optimal treatment effectiveness, sufficient treatment coverage, and improvements in sanitation act synergistically to minimize infection and reinfection risks. Over a multi-year horizon, these combined interventions significantly reduced disease prevalence in endemic populations. This study demonstrates that integrating mathematical analysis with practical interventions provides a robust model for understanding typhoid dynamics. By identifying the parameters most critical to disease reduction, the seitrb model offers evidence-based guidance for health practitioners in designing localized and sustainable typhoid control strategies. Overall, the model highlights the transformative role of coordinated vaccination, treatment, and sanitation in achieving effective prevention and long-term community health improvement.
Dimensi Metrik Lokal pada Operasi Korona Graf Ular Segitiga dengan Graf Lintasan Orde Dua Zuha, Jaqueline Widad; Rahmadi, Deddy; Munandar, Arif
JURNAL DIFERENSIAL Vol 8 No 1 (2026): April 2026
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v8i1.27365

Abstract

Graphs were first introduced by Leonard Euler through the Königsberg Bridge problem in 1736. Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. The concept of distance in graphs leads to the notions of metric dimension and local metric dimension. Let $W \subset V(G)$ with $W = \{w_1, w_2, \dots, w_n\}$. The representation of a vertex $x \in V(G)$ with respect to $W$ is defined by $r(x \mid W) = (d(x, w_1), d(x, w_2), \dots, d(x, w_n)).$ The set $W$ is called a local resolving set of $G$ if for every pair of adjacent vertices $u, v \in V(G)$, $r(u \mid W) \ne r(v \mid W)$. The minimum cardinality of such a set is called the local metric dimension of $G$ and is denoted by $\dim_{\ell}(G)$. This research aims to determine the metric dimension and local metric dimension of the triangular snake graph $T_n$, as well as graphs obtained from the corona operation between $T_n$ and a path graph of order two. The method used is a literature study with an analysis of graph structure and vertex distances. The results show that both the metric dimension and the local metric dimension of the triangular snake graph are equal to $2$. Moreover, the local metric dimension of $T_n \odot P_2$ is $2n+1$, while that of $P_2 \odot T_n$ is $n+3$ for odd $n$ and $n+2$ for even $n$.

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