This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...

In this paper, we investigate the properties of various relations, operators and upper sets on partially ordered sets. Mathematics Subject Classification: 03E72, 54A40, 54B10

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

First, we establish a useful characterization of effective sets in conditionally complete partially ordered sets. Then, we prove that each maximal nonexpansive partial multiplier on a conditionally complete and infinitely distributive partially ordered set with upper bounded centre is inner. Finally, we show that some analogous results hold for T1-families of sets partially ordered by inclusion.