Abstract Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work appropriate for capturing market fluctuations which random white noise has the potential to accurately estimate put option premiums while providing good numerical convergence. aim of pape...

‎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...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

We present an exact Mixed Integer Programming (MIP) solution scheme where a set covering model is used to find a small set of first-choice branching variables. In a preliminary “sampling” phase, our method quickly collects a number of relevant lowcost fractional solutions that qualify as obstacles for the Linear Programming (LP) relaxation bound improvement. Then a set covering model is solved ...

We discuss a model of X-ray variability of active galactic nuclei (AGN). We consider multiple spots which originate on the surface of an accretion disk following intense irradiation by coronal flares. The spots move with the disk around the central black hole and eventually decay while new spots continuously emerge. We construct time sequences of the spectra of the spotted disk and compute the ...

Although the cross-sectional relationship of arterial stiffness with cerebral small vessel disease is consistently shown in middle-aged and young-old adults, it is less clear whether these associations remain significant over time in very old adults. We hypothesize that arterial stiffness is longitudinally associated with white matter characteristics, and associations are stronger within waters...

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable whose distribution is just the Bose distribution yielding the Planck’s law of black-body radiation. The fractional...