Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

Abstract

In this paper, we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces. Furthermore, we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated with S λ and consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations. We also establish certain interesting examples to illustrate the usability of our results.

Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations

“…􏼈 􏼉 is a sequence of iterates obtained from the K * -iterative process (1). Subsequently,lim n ⟶ ∞ ‖x n − a * ‖ exists for each a * ∈ D A .…”

“…􏼈 􏼉 is a sequence of iterates obtained from the K * -iterative process (1). Subsequently, x n 􏼈 􏼉 is strongly convergent to a point of D A ifA satisfes condition (I).…”

“…In recent years, theory of fxed points gained the attention of many authors [1,2]. Whenever the ordinary analytical techniques cannot yield a solution to a diferential or an integral equation, we are interested in fnding the approximate value of the requested solution (see, e.g., the recent results in [3][4][5] and others).…”

“…Tey demonstrated that among the many other iterative processes, the K * iteration (1) gives very high accurate results in very less steps of iterations in the setting of Suzuki mappings. We improve here their results to the larger class of generalized α-nonexpansive mappings.…”