Convergence analysis of a novel iteration process with application to a fractional differential equation

Abstract

The objective of this article is to study a three-step iteration process in the framework of Banach spaces and to obtain convergence results for Suzuki generalized nonexpansive mappings. We also provide numerical examples that support our main results and illustrate the convergence behavior of the proposed process. Further, we present a data-dependence result that is also supported by a nontrivial numerical example. Finally, we discuss the solution of a nonlinear fractional differential equation by utilizing our results.

A New Robust Iterative Scheme Applied in Solving a Fractional Diffusion Model for Oxygen Delivery via a Capillary of Tissues

“…Let B = R. We define a mapping T : B → B by T x = 3x+2 4 which is a contraction mapping with the contraction constant δ = 3 4 and F (T ) = {2}. If we choose α n = β n = γ n = 3 4 , then it is clear from Tables 1 and 2 and Figures 1 and 2 that our iterative scheme converges to the fixed point, 2, faster than all of the CR [10] as in (4), F* [14] as in (8), Picard-S [11] as in (5), Modified-SP [14] as in (9), Uddin et al [13] as in (7) and Picard-Ishikawa [15] as in (10)…”

“…which was used to approximate the solution to a delay fractional differential equation. Uddin et al [13], in 2022, introduced the following iterative scheme:…”

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

“…Many researchers have studied this topic because it has many applications. Related to this matter, we suggest the recent literature [29][30][31][32][33][34][35] and the references therein.…”