Tripled Fixed Points and Existence Study to a Tripled Impulsive Fractional Differential System via Measures of Noncompactness

In this paper, a tripled fractional differential system is introduced as three associated impulsive equations. The existence investigation of the solution is based on contraction principle and measures of noncompactness in terms of tripled fixed point and modulus of continuity. Our results are valid for both Kuratowski and Hausdorff measures of noncompactness. As an application, we apply the obtained results to a control problem.

The dynamic analysis on a class of stochastic impulsive equations with doubly weighted pseudo almost automorphic coefficients on time scales

Devoting to exploring the translation invariance and convolution invariance of doubly weighted pseudo almost automorphic stochastic processes with impulses on time scales proposed in this paper. Based on these results, taking advantage of a new approach to obtain the existence and uniqueness of the doubly weighted pseudo almost automorphic solutions to a class of stochastic nonlinear impulsive equations on time scales, which enrich the dynamics of doubly weighted pseudo almost automorphic stochastic processes. Finally, an example is researched to illustrate our conclusions.