In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo’s fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp.

Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of integral Maxwell equation, the simple examples of the fields of homogeneous fractal distribution are considered. The...

The weak limit is derived of the sample covariance of a pair of fractionally integrated processes, one I(dY ) for −2 < dY < 12 , and the other I(1 + dX) for −2 < dX < 12 . The stochastic component (mean deviation) of the limit has the representation of a RiemannLiouville fractional integral of a functional of regular Brownian motion, B, having the form φ(t) = R t 0 XdB. In the case dX < 0, the ...

This paper investigates the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with Riemann-Liouville fractional integral boundary conditions. By applying a variety of fixed point theorems, combining with a new inequality of fractional order form, some sufficient conditions are established. Some examples are given to illustrate our results....

This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory. © 2015 Elsevie...

The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graph...

In this paper a novel Hybrid Differential Artificial Bee Colony Algorithm (HDABCA) has been proposed for designing a fractional order proportional-integral (FO-PI) speed controller in a Permanent Magnet Synchronous Motor (PMSM) drive. FO-PI controllers’ parameters involve proportionality constant, integral constant and integral order, and hence its design is more complex than that of the usual ...

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...

Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...

The metric polytope ,//~. is defined by the triangle inequalities: xij-Xik-Xjk <~ 0 and xii + Xik + Xjk ~< 2 for all triples i,j, k of(1 ..... n}. The integral vertices of ~¢¢~. are the incidence vectors of the cuts of the complete graph Kn. Therefore, ~¢~. is a relaxation of the cut polytope of K~. We study here the fractional vertices of ~¢¢~. Many of them are constructed from graphs; this is...