In this paper, we consider fractional Liu process. First, the membership functions, expected values and variances of arithmetic and geometric fractional Liu process are given. Then we suppose that stock price follows geometric fractional Liu process and formulate fractional Liu’s stock model. Based on this model, European option pricing formulas are obtained.

In this paper, a fractional-order model of the gas film is proposed for dynamic characteristics an air bearing. Based on common between and viscoelastic body, idea equivalent modeling presented to improve accuracy. Four (FOGF) models are introduced based generalization traditional models. The analysis FOGF shows that can capture more complex fit real data better than A genetic algorithm particl...

Based on an idea of Granger (1986), we analyze a new vector autoregressive model de…ned from the fractional lag operator 1 (1 L)d: We …rst derive conditions in terms of the coe¢ cients for the model to generate processes which are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process Xt of order d; d > 0; for which there are vectors so tha...

In this paper, the authors considered a class of fractional-order Hindmarsh-Rose (HR) neuron model with time-delays and widely investigated the dynamical behaviors of considered fractional-order HR model with time-delays. Some new sufficient conditions are derived by using the proposed stability theory of linear fractional-order systems to guarantee the stability results of fractional-order HR ...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

Fractional calculus is about the integration or differentiation of non-integer orders. The use of “fractional” is purely due to historical reasons [1]. Using fractional order differential equations is believed to be able to better characterize the nature around us. Using an integer order model is only for our own convenience. Depending on the scale on which we characterize the dynamics of a sys...

The absorption of compressional and shear waves in many viscoelastic solids has been experimentally shown to follow a frequency power law. It is now well established that this type of loss behavior can be modeled using fractional derivatives. However, previous fractional constitutive equations for viscoelastic media are based on temporal fractional derivatives. These operators are non-local in ...

Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, the model is formulated in terms of a fractional integration of stochastic processes.

We investigate heterotic string-type model-building for the recently-proposed fractional superstring theories. We concentrate on the cases with critical spacetime dimensions four and six, and find that a correspondence can be drawn between the new fractional superstring models and a special subset of the traditional heterotic string models. This allows us to generate the partition functions of ...