In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (1<α≤2) Vibration Equation (VE) of large membranes with the use of an iterative technique namely Residual Power Series Method (RPSM). The fractional derivative is defined in the Caputo sense. Example problems have been solved to demonstrate the efficacy of the present method and ...

In order to define the discrete fractional Fourier transform, Hermite Gauss-like eigenvectors are needed and one way of extracting these eigenvectors is to employ DFT commuting matrices. Recently, Pei et al. exploited the idea of obtaining higher order DFT-commuting matrices, which was introduced by Candan previously. The upper bound of O(h) approximation to N N commuting matrix is 2kþ1rN in Ca...

In this paper, we develop some methods to save the bandwidth required in the fractional domain. The fractional domain is the transformed domain of the fractional Fourier transform (FRFT). It is the intermediate of the time domain and the frequency domain. We find that, with the aid of the fractional Hilbert transform and other techniques, we can save 112 or 314 of the bandwidth in the fractiona...

This paper presents a Taylor series approach for solving linear fractional de-centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with asingle decision maker at the upper level and multiple decision makers at the lower level.In the proposed approach, the membership functions associated with each objective(s) ofthe level(s) of LFDBL-MODM are transformed by using a Taylor s...

4. Course Outline: (i) Review of Linear ARMA/ARIMA Time Series Models and their Properties. (ii) An Introduction to Spectral Analysis of Time Series. (iii) Fractional Differencing and Long Memory Time Series Modelling. (iv) Generalized Fractional Processes. Gegenbaur Processes. (v) Topics from Financial Time Series/Econometrics: ARCH and GARCH Models. (vi ) Time Series Modelling of Durations: A...

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination transformation and technique, we achieve analytic approximation results in rapid convergent form by employing notion limit, with less time effort than method. Three challen...