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Kajian Perbandingan Turunan dan Integral Fraksional Riemann–Liouville, Caputo, dan Konformabel serta Aplikasinya Gunawan, Gani; Rusyaman, Endang; Sukono, Sukono; Carnia, Ema
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.68569.245-258

Abstract

Penelitian ini membandingkan tiga definisi utama turunan fraksional, yaitu Riemann–Liouville, Caputo, dan Konformabel, dalam pemodelan sistem dinamis yang melibatkan efek memori. Populasi kajian adalah operator turunan fraksional sebagai generalisasi kalkulus klasik berorde bukan bilangan bulat. Intervensi dilakukan melalui pendekatan analitik dan numerik, meliputi kajian sifat dasar operator, analisis eksistensi solusi, dan penerapannya pada persamaan diferensial fraksional linear sederhana. Perbandingan difokuskan pada kesesuaian terhadap sifat kalkulus klasik, bentuk solusi, dan karakter peluruhan sistem. Hasil menunjukkan bahwa turunan Riemann–Liouville dan Caputo menghasilkan solusi berbasis fungsi Mittag–Leffler dengan peluruhan lambat, sehingga sesuai untuk fenomena dengan memori jangka panjang, sedangkan turunan Konformabel menghasilkan solusi eksponensial dengan peluruhan lebih cepat dan efisiensi komputasi yang lebih tinggi. Rentang waktu kajian difokuskan pada orde fraksional α = 1/2 sebagai representasi perilaku umum ketiga definisi. Temuan ini menegaskan bahwa pemilihan operator fraksional harus disesuaikan dengan tujuan analisis dan konteks aplikasi, khususnya antara kebutuhan representasi efek memori dan efisiensi analitik
Optimization Model for Agricultural Processed Products Supply Chain Problem in Bandung During Covid-19 Period Zahrani Irmansyah, Athaya; Chaerani, Diah; Rusyaman, Endang
Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri Vol. 23 No. 2 (2021): Dec 2021
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.9744/jti.23.2.83-92

Abstract

Coronavirus disease, commonly called Covid-19, is a virus that causes a pandemic in almost every country globally. One of those countries is Indonesia, which has many big cities with dense populations. This study was conducted in Bandung, the capital of West Java, Indonesia. As a result of the Covid-19 pandemic, Bandung was seriously affected in various ways. One was the disruption in the distribution of the agricultural processed products supply chain, which changes producers and consumers' behaviour. Furthermore, as an effort by the government to break the spread of the virus, health protocols limit the distribution. The purpose of this study is to design an optimization model for the supply chain problem of agricultural processed products in Bandung during the Covid-19 period with the objective function is maximizing product suppliers so that all demands on consumers are fulfilled. The use of Local Food Hub (LFH) is a help in this research as a distribution centre point between the producer zone and the consumer zone. Finally, numerical experiments were carried out in two scenarios, namely Large-scale Social Distancing (LSD) and Partial Social Distancing (PSD). It was found that the optimal distribution solution was obtained if the PSD scenario was applied.
THE GARCH MODEL VOLATILITY OF SHARIA STOCKS ASSOCIATED CAUSALITY WITH MARKET INDEX Endang Soeryana Hasbullah; Endang Rusyaman; Alit Kartiwa
International Journal of Quantitative Research and Modeling Vol. 1 No. 1 (2020): International Journal of Quantitative Research and Modeling
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v1i1.3

Abstract

The purpose of this paper is to examine the volatility of Islamic stocks related to the causality of the composite stock price index (CSPI). The aim is to investigate the causality of several levels of stock returns with the movement of the CSPI, and determine its volatility as a measure of risk. To determine the causality relationship is done by using the granger causality test method, with Vector Autoregressive (VAR) modeling. Whereas to determine the volatility is done using the Generalized Autoregressive Conditional Heteroscedastisiy (GARCH) model approach. The results of the causality test show that there is a direct relationship that affects and is influenced by the CSPI, and the relationship that affects each other between the company's stock market and the movement of the CSPI. While the volatility follows the GARCH model (1, 1). Based on the results of this study are expected to be used as consideration in making investment decisions in the analyzed stocks.
Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation Abiodun Ezekiel Owoyemi; Ira Sumiati; Endang Rusyaman; Sukono Sukono
International Journal of Quantitative Research and Modeling Vol. 1 No. 4 (2020): International Journal of Quantitative Research and Modeling
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v1i4.83

Abstract

Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the economic and financial fields. Laplace decomposition method is one of the reliable and effective numerical methods for solving fractional differential equations. Thus, this paper aims to apply the Laplace decomposition method for solving the fractional Black-Scholes equation, where the fractional derivative used is the Caputo sense. Two numerical illustrations are presented in this paper. The results show that the Laplace decomposition method is an efficient, easy and very useful method for finding solutions of fractional Black-Scholes partial differential equations and boundary conditions for European option pricing problems.