Bachok M. Taib

Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.

Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order

This paper presents the application of homotopy perturbation and variational iteration methods as numerical methods for Fredholm integrodifferential equation of fractional order with initial-boundary conditions. The fractional derivatives are described in Caputo sense. Some illustrative examples are presented.

Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense. To show the efficiency of the considered method, some examples that include the fractional Klein-Gordon equation, fractional Burgers equation, and fractional Black-Scholes equation are investigated.

The Improved Models of Internet Pricing Scheme of Multi Service Multi Link Networks with Various Capacity Links

Internet Service Providers (ISPs) nowadays deal with high demand to promote good quality information. However, the knowledge to develop new pricing scheme that serve both customers and supplier is known, but only a few pricing plans involve QoS networks. This study will seek new proposed pricing plans are offered with multi service multi link networks involved. The multi service multi link Networks scheme is solved as an optimization model by comparing two models in multi QoS networks. The results showed that by fixing the base price and varying the quality premium or varying the base price and quality and setting up the equal capacity link values, ISP achieved the goal to maximize the profit.

Note on the Convergence Analysis of Homotopy Perturbation Method for Fractional Partial Differential Equations

We apply the homotopy perturbation method to obtain the solution of partial differential equations of fractional order. This method is powerful tool to find exact and approximate solution of many linear and nonlinear partial differential equations of fractional order. Convergence of the method is proved and the convergence analysis is reliable enough to estimate the maximum absolute truncated error of the series solution. The fractional derivatives are described in the Caputo sense. Some examples are presented to verify convergence hypothesis and simplicity of the method.

Designing a New Model for Worm Response Using Security Metrics

Nowadays, worms are becoming more sophisticated, intelligent and hard to be detected and responded than before and it becomes as one of the main issues in cyber security. It caused loss millions of money and productivities in many organizations and users all over the world. Currently, there are many works related with worm detection techniques but not much research is focusing on worm response. Therefore, in this research paper, a new model to respond to the worms attack efficiently is built. This worm response model is called as eZSiber, inspired by apoptosis or also known as cell-programmed death. It is a concept borrowed from human immunology system (HIS), where it has been mapped into network security environment. Once the user’s computer detects any indication of the worm attacks, the apoptosis is triggered. In order to trigger the apoptosis, security metrics plays a very important role in identifying the weight and the severity of the worm attacks. In this model, the static and dynamic analyses were conducted and the machine learning algorithms were applied to optimize the performance. Based on the experiment conducted, it produced an overall accuracy rate of 99.38 % using Sequential Minimal Optimization (SMO) algorithm. This performance criteria result indicated that this model is an efficient worm response model.

Designing a New Model for Trojan Horse Detection Using Sequential Minimal Optimization

Malwares attack such as by the worm, virus, trojan horse and botnet have caused lots of troublesome for many organisations and users which lead to the cybercrime. Living in a cyber world, being infected by these malwares becoming more common. Nowadays the malwares attack especially by the trojan horse is becoming more sophisticated and intelligent, makes it is harder to be detected than before. Therefore, in this research paper, a new model called Efficient Trojan Detection Model (ETDMo) is built to detect trojan horse attacks more efficiently. In this model, the static, dynamic and automated analyses were conducted and the machine learning algorithms were applied to optimize the performance. Based on the experiment conducted, the Sequential Minimal Optimization (SMO) algorithm has outperformed other machine learning algorithms with 98.2 % of true positive rate and with 1.7 % of false positive rate.

Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order

We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.

On the symbolic manipulation for the cardinality of certain degree polynomials

The research on cardinality of polynomials was started by Mohd Atan [1] when he considered a set, V(f_;pα)={umodpα:f_(u)≅0modpα}, where α > 0 and f_=(f1,f2,⋯fn). The term f_(u)≅0_modpα means that we are considering all congruence equations of modulo pα and we are looking for u that makes the congruence equation equals zero. This is called the zeros of polynomials. The total numbers of such zeros is termed as N(f_;pα). The above p is a prime number and Zp is the ring of p-adic integers, and x_=(x1,x2, ⋯xn). He later let N(f_;pα)=card V(f_;pα). The notation N(f_;pα) means the number of zeros for that the polynomials f_. For a polynomial f (x) defined over the ring of integers Z, Sandor [2] showed that N(f;pα)≤ mp12ordpD, where D ≠ 0, α > ordpD and D is the discriminant of f. In this paper we will try to introduce the concept of symbolic manipulation to ease the process of transformation from two-variables polynomials to one-variable polynomials.

Numerical Methods for Fractional Order Singular Partial Differential Equations with Variable Coefficients

We implement relatively analytical methods, the homotopy perturbation method and the variational iteration method, for solving singular fractional partial differential equations of fractional order. The process of the methods which produce solutions in terms of convergent series is explained. The fractional derivatives are described in Caputo sense. Some examples are given to show the accurate and easily implemented of these methods even with the presence of singularities.