In this paper, we investigate existence, uniqueness and four different types of Ulam’s stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers- Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and Krasnosel’ski i’s fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.
Recently we investigated a type of Hyers-Ulam stability of the Schrodinger equation with the symmetric parabolic wall potential that efficiently describes the quantum harmonic oscillations. In this paper we study a type of Hyers-Ulam stability of the Schrodinger equation when the potential barrier is a quartic wall in the solid crystal models.
Abstract. The aim of this paper is to establish common fixed point theorems under generalized ( ψ − φ )-weak contractions in the setting of complete S -metric spaces and we support our result by some examples. Also an application of our results, we obtain some fixed point theorems of integral type. Our results extend Theorem 2.1 and 2.2 of Doric [5], Theorem 2.1 of Dutta and Choudhury [6], and many other several results from the existing literature.
In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Fi- nally, we give some applications of our results in discrete and functional fractional economic systems.
The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b -metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b -metric spaces.
