This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study existence mild solutions under situation that relevant semigroup is and nonlinear term satisfies more general growth conditions instead Lipschitz-type conditions. Moreover, by establishing Gronwall-type integ...

We construct global dissipative solutions on the torus of dimension at most three defocusing isothermal Euler–Langevin–Korteweg system, which corresponds to Euler–Korteweg system compressible quantum fluids with an pressure law and a linear drag term respect velocity. In particular, feature prevents energy BD-entropy from being positive. Adapting standard approximation arguments we first show e...

In this paper, to begin with, we introduce the concept of Besicovitch almost periodic stochastic processes in distribution sense and study relationship between it $ p $-th mean sense. addition, take a class Clifford-valued neural networks with time-varying delays as an example investigate existence uniqueness solutions by using Banach fixed point theorem variant Gronwall lemma. Moreover, global...

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.

*Correspondence: [email protected] 2College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China 3Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, 710049, China Full list of author information is available at the end of the article Abstract This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg ...

Abstract In this research, we first investigate the existence of solutions for a new fractional boundary value problem in Liouville–Caputo setting with mixed integro-derivative conditions. To do this, Kuratowski’s measure noncompactness and Sadovskii’s fixed point theorem are our tools to reach aim. sequel, discuss continuous dependence on parameters by means generalized Gronwall inequality. Mo...