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This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market. Using call-and-pull options, investors can theoretically decide when to sell, hold, or buy shares for maximum profits. However, the process of forming the Black–Scholes model uses a normal distribution, where, in reality, the call option formula obtained is less realistic in the stock market. Therefore, it is necessary to modify the model to make the option values obtained more realistic. In this paper, the method used to determine the solution to the modified Fractional Black–Scholes equation is a combination of the finite difference method and the fractional differential transformation method. The results show that the combined method of finite difference and fractional differential transformation is a very good approximation for the solution of the Fractional Black–Scholes equation. [ABSTRACT FROM AUTHOR]

The main objective of this study is to determine the existence and uniqueness of solutions to the fractional Black–Scholes equation. The solution to the fractional Black–Scholes equation is expressed as an infinite series of converging Mittag-Leffler functions. The method used to discover the new solution to the fractional Black–Scholes equation was the Daftardar-Geiji method. Additionally, the Picard–Lindelöf theorem was utilized for the existence and uniqueness of its solution. The fractional derivative employed was the Caputo operator. The search for a solution to the fractional Black–Scholes equation was essential due to the Black–Scholes equation's assumptions, which imposed relatively tight constraints. These included assumptions of a perfect market, a constant value of the risk-free interest rate and volatility, the absence of dividends, and a normal log distribution of stock price dynamics. However, these assumptions did not accurately reflect market realities. Therefore, it was necessary to formulate a model, particularly regarding the fractional Black–Scholes equation, which represented more market realities. The results obtained in this paper guaranteed the existence and uniqueness of solutions to the fractional Black–Scholes equation, approximate solutions to the fractional Black–Scholes equation, and very small solution errors when compared to the Black–Scholes equation. The novelty of this article is the use of the Daftardar-Geiji method to solve the fractional Black–Scholes equation, guaranteeing the existence and uniqueness of the solution to the fractional Black–Scholes equation, which has not been discussed by other researchers. So, based on this novelty, the Daftardar-Geiji method is a simple and effective method for solving the fractional Black–Scholes equation. This article presents some examples to demonstrate the application of the Daftardar-Gejji method in solving specific problems. [ABSTRACT FROM AUTHOR]

In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model's basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three equilibrium points: the trivial equilibrium point, the equilibrium point where there is no harvest, and the co-existing equilibrium point. The local and global stability of each equilibrium point of the model is explored. Moreover, the interior equilibrium point is always globally asymptotically stable, and the system experiences no limit cycles around the interior equilibrium point. Numerical simulations are conducted to illustrate the theoretical results obtained. Finally, we find overlapping conditions regarding the dynamics between the model we developed and a model that considers a constant critical biomass level for certain parameters. [ABSTRACT FROM AUTHOR]

This paper reports the finding of a new financial chaotic system. A new control law for completely synchronizing the new financial chaotic system with itself has been established using adaptive integral sliding mode control. We also find that the new financial chaotic system has fascinating traits including symmetry, equilibrium points, multistability, Lyapunov exponents and bifurcation diagrams. We illustrate all the main results of this research work using MATLAB phase plots. The Lyapunov characteristic exponents and analysis using bifurcation diagrams have resulted in a new financial chaos system showing chaos phenomena in the intervals of parameters 0 < a < 15, and parameters 0 < b < 0.25. The results of this study can be used to predict if there is chaos in financial risk. Chaotic systems have many applications in engineering like cryptosystems and secure communication systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Viscosity is a measure which represents the magnitude of a moving fluid. Meanwhile, the surface tension of a fluid is the stretched elastic tendency of the fluid due to the attraction force between the molecules. Previous studies are interested in the fluid mechanics problem presenting the relationship between the viscosity and surface tension in both linear and exponential models. The aim of this study is to present the the discourse about the fractional relationship in the form of fractional differential equation model based on the empirical data of the measurement of surface tension and viscosity of lubricating oil in the laboratory. To find solution of fractional differential equation, Laplace transform and Mittag-Lefler function are used. The output of this research is a proposed fractional model and some graphs showing the relationship between them. [ABSTRACT FROM AUTHOR]

Black-Scholes partial differential equation is a very well-known model for pricing European option with the underlying financial assets being the stock price. The combination of the Adomian decomposition method and Laplace transform is called the Laplace-Adomian decomposition method. This method is effective and easy to solve ordinary or partial differential equations. Therefore, the purpose of this paper is to find the solution to the Black-Scholes equation using the Laplace-Adomian decomposition method (LADM). The results show that LADM is able and powerful to solve the Black-Scholes equation. Furthermore, the solution obtained is used to build a call and put option price model. The numerical simulation shows that the proposed model is very useful for pricing option properly and accurately. [ABSTRACT FROM AUTHOR]

In this paper the Adjustable Robust Maximum Flow Problem (ARMFP) is discussed. The problem is considered as a two-stage optimization problem with two kinds of variables, i.e., adjustable and non-adjustable variables. There is also an assumption that the input parameter, i.e. arc capacities, lie within an uncertainty set. The main challenge in Adjustable Robust Optimization (ARO) is to find whether the robust counterpart of ARMFP be can be formulated into a computationally tractable optimization problem. To this end, a convex continue set is assumed to be the set of the adjustable variables and or the uncertain arc capacities. In this paper it is considered the parametric ellipsoidal and polyhedral uncertainty set. The ARMFP is constructed by defining the maximum flow for the whole network represented by a flow xts that connect the destination node t back to the source node s. This xts is assumed to be the adjustable variable. In the case of parametric ellipsoidal uncertainty, the characteristic of ARMFP is analysed using the Theorem of Max-Flow and Min- Cut. In the case of polyhedral uncertainty set, the counterpart is obtained as a linear programming problem. Some examples are presented. [ABSTRACT FROM AUTHOR]