The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. Schauder’s fixed point Theorem is the main tool used here to establish the existence ...

In the current paper, some existence and uniqueness results for a generalized proportional Hadamard fractional integral equation are established via Picard Picard-Krasnoselskii iteration methods together with Banach contraction principle. A simulative example was provided to verify applicability of theoretical findings.

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

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach ...

*Correspondence: [email protected] 1Department of Mathematics, Çankaya University, Ankara, 06530, Turkey Full list of author information is available at the end of the article Abstract We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (I...