We established some new fractional integral inequalities of Ostrowski-type for functions of two independent variables whose second order mixed partial derivatives in absolute value to some powers are s -convex on the coordinates. These results are obtained by using generalized Katugampola-type fractional integrals for functions of two independent variables. Our results generalizes some results in the literature.

Recently, the dynamical behaviors of a fractional order three species food chain model was studied by Alidousti and Ghahfarokhi (Nonlinear Dynamics, doi: org/10

In this paper, we are concerned with a class of fractional Hamiltonian systems containing right Riemann-Liouville fractional derivatives and left Caputo fractional derivatives with impulsive effects. Under certain conditions, the existence of solutions are obtained for this class of systems by means of the least action principle, the saddle point theorem as well as some skills of inequalities. One of the innovations of this paper is that the variational functional of these problems are established in a proper fractional derivative space. Moreover, in order to show the feasibility and effectiveness of our results, we present two examples.

This paper is devoted to the study of the existence and uniqueness of solutions to a boundary value problem for nonlinear Hadamard fractional differential equations with nonlocal multi-point boundary conditions.The results are obtained by using a variety of fixed point theorems.The paper concludes with some illustrative examples.

Firstly, the surveys for studies on boundary value problems for higher order ordinary differential equations and for higher order fractional differential equations are given.Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented.Thirdly we propose four classes of higher order linear fractional differential equations and give their exact piecewise continuous solutions.Fourthly we propose some new classes of boundary value problems for higher order fractional differential equations with impulse effects.Fifthly we establish new general methods for converting boundary value problems of impulsive fractional differential equations with the Riemann-Liouville fractional derivatives or Caputo fractional derivatives to equivalent integral equations.Sixthly by employing fixed point theorems in Banach space, we establish new existence results of solutions for these boundary value problems.Seventh, some remarks are given to show that many methods in known papers are un-suitable.Eighth, some examples are presented to illustrate the efficiency of the results obtained.Finally, possible trends of researches are given at the end of the paper.

In this paper, the representation of solution to linear inhomogeneous Caputo fractional differential equation with continuous variable coefficient has been considered by using Green function.We have proved that the solution of linear inhomogeneous equations with homogeneous initial condition can be represented by using classical Green function, generalized Green function and modified Green function.

We establish the unique solvability in Hlder spaces for an initial-boundary problem for fractional diffusion equation with fractional dynamic boundary condition.

In this paper, we determine the eigenvalues i , 1 i n, for which there exist positive solutions for the iterative system of fractional order three-point boundary value problems by applying fixed point theorem.

The purpose is to study the Cauchy problem for non-linear in time and space pseudo-differential equations. These include the fractional in time versions of HJB equations governing the controlled scaled CTRW. As a preliminary step which is of independent interest we analyse the corresponding linear equation proving its well-posedness and smoothing properties.

Thispaper presents improvements ofsome Opial-type inequalities involving the Riemann- Liouville, Caputo and Canavati fractional derivatives, and presents some new Opial-type inequal- ities.