The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the s...

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.

We study the boundary value problem for a kind N-dimension nonlinear fractional differential system with the nonlinear terms involved in the fractional derivative explicitly. The fractional differential operator here is the standard Riemann-Liouville differentiation. By means of fixed point theorems, the existence and multiplicity results of positive solutions are received. Furthermore, two exa...

In recent years, notable contributions have been made to both the theory and applications of the fractional differential equations. These equations are increasingly used to model problems in research areas as diverse as population dynamics, mechanical systems, fiber optics, control, chaos, fluid mechanics, continuous-time random walks, anomalous diffusive and subdiffusive systems, unification o...

To describe the ability of image fractional differential in texture detail enhancement and to study the lateral inhibition principle, multiform masks for digital image fractional differential and their operation rules are discussed. The theoretical basis of fractional differential in modulation and demodulation is also analyzed. Through the derivation on the relation between fractional differen...

In this paper a countable family of new compactly supported non-Haar p-adic wavelet bases in L(Q p ) is constructed. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional...

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...

In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conducti...