Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

In the present work we discuss the existence of solutions for a system of nonlinear fractional integro-differential equations with initial conditions. This system involving the Caputo fractional derivative and Riemann−Liouville fractional integral. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.

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...

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...