Abstract In this paper we study fractional initial value problems with Caputo–Fabrizio derivative which involves nonsingular kernel. First apply α - ℓ -contraction and -type F mappings to the existence uniqueness of solutions for such problems. Finally, use some contraction in complete $\mathfrak{F}$ F -metri...

A weakly o-minimal structure M = (M,≤,+, . . .) expanding an ordered group (M,≤, +) is called non-valuational iff for every cut 〈C,D〉 of (M,≤) definable in M, we have that inf{y − x : x ∈ C, y ∈ D} = 0. The study of non-valuational weakly o-minimal expansions of real closed fields carried out in [MMS] suggests that this class is very close to the class of o-minimal expansions of real closed fie...

Abstract In this paper, we introduce two new concepts of F -contraction, called dual $F^{*}$ F ∗ -weak contraction and triple contraction, which generalize the existing contractions in sense Wardowski, Jleli Samet as well Skof. These generalizations embed their roots ai...

The well-known Banach’s fixed point theorem asserts that if D = X, f is contractive and (X, d) is complete, then f has a unique fixed point in X. In nonlinear analysis, the study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been investigated deeply. The Banach contraction principle [1] is one of the initial and crucial results in thi...

in this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .