In this note, we define an operator on a space of Itô processes, which call Caputo-Itô derivative, then considerer Cauchy problem for stochastic fractional differential equation with derivative. We demonstrate the existence and uniqueness by contraction mapping argument some examples are given.

In this paper, we obtain the existence of unique solution anti-periodic type (anti-symmetry) integral multi-point boundary conditions for sequential fractional differential equations. We apply Banach contraction mapping principle to get desired results. Our results specialize and extend some existing

In this paper, we extend the idea of α-ψ contraction mapping to product spaces by introducing Prešić–Ćirić-type contractions and utilize them prove some coincidence common fixed-point theorems in context ordered metric using α-admissibility mapping. Our newly established results generalize a number well-known from literature. Moreover, give examples that attest credibility our results. Further,...

Interpolative Kannan contractions are a refinement of contraction, which is considered as one the significant notions in fixed point theory. Gb-metric spaces generalized concept both concepts b-metric and G-metric therefore, common results contraction based on this resultsfor concepts. The purpose manuscript, to take advantage interpolative together with notion Ωb equipped H simulation function...

Abstract In this paper, a class of nonlinear ? -Hilfer fractional integrodifferential coupled systems on bounded domain is investigated. The existence and uniqueness results for the are proved based contraction mapping principle. Moreover, Ulam–Hyers–Rassias, Ulam–Hyers, semi-Ulam–Hyers–Rassias stabilities to initial value problem obtained.

The last few hours of human pregnancy are characterized by uterine contractions that effect dilatation of the cervix and force the fetus through the birth canal. The myometrial contractions of labor are painful, which is why the term labor pains is used to describe this process. Before these forceful, painful contractions begin, however, the uterus must be prepared for labor. During the first 3...

If (X, d) is a complete metric space and T : X → X is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of T starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader...

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

A.2. Contraction lemma The following is a version of Talagrand’s contraction lemma (Ledoux & Talagrand, 2011). Since our definition of Rademacher complexity does not use absolute values, we give an explicit proof below. Lemma 8. Let H be a hypothesis set of functions mapping X to R and Ψ1, . . . ,Ψm, μ-Lipschitz functions for some μ > 0. Then, for any sample S of m points x1, . . . , xm ∈ X , t...