On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives

Abstract

Please cite this article as: J. Wang, Y. Zhang, On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives, Appl. Math. Lett. (2014), http://dx.Abstract In this paper, a class of nonlinear fractional order differential impulsive systems with Hadamard derivative is discussed. Firstly, a reasonable concept on the solutions of fractional impulsive Cauchy problems with Hadamard derivative and the corresponding fractional integral equations are established. Secondly, two fundamental existence results are presented by using standard fixed point methods. Finally, two examples are given to illustrate our theoretical results.

Unique solutions for a new coupled system of fractional differential equations

“…Different boundary conditions of coupled systems can be found in the discussions of some problems such as Sturm-Liouville problems and some reaction-diffusion equations (see [26,27]), and they have some applications in many fields such as mathematical biology (see [28,29]), natural sciences and engineering; for example, we can see beam deformation and steady-state heat flow [30,31] and heat equations [14,32,33]. So nonlinear coupled systems subject to different boundary conditions have been paid much attention to, and the existence or multiplicity of solutions for the systems has been given in literature, see [4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24][25] for example. The usual methods used are Schauder's fixed point theorem, Banach's fixed point theorem, Guo-Krasnosel'skii's fixed point theorem on cone, nonlinear differentiation of Leray-Schauder type and so on.…”

Influence of Fractional Differential on Correlation Coefficient between EC1:5 and Reflectance Spectra of Saline Soil

“…After holding the First Conference on Fractional Calculus and its Applications on June 1974 [17], the fractional calculus has been widely applied in various fields [18][19][20][21][22][23][24][25][26], because the fractional models are more accurate than the integer ones. In the field of remote sensing, fractional calculus is mainly used for image enhancement and feature extraction [27][28][29][30].…”

On a nonlinear Hadamard type fractional differential equation with p-Laplacian operator and strip condition

“…Although many researchers are paying more and more attention to Hadamard type fractional differential equation, the study of the topic is still in its primary stage. About the details and recent developments on Hadamard fractional differential equations, we refer the reader to [1,4,5,24,34,39].…”