Computational Approaches for a New Iterative Process With Applications in Signal Processing and Caputo‐Type Nonlinear Fractional Differential Equations
Danish Ali, Mujahid Abbas, Cristian Ciobanescu
Source abstract
ABSTRACT This paper introduces an efficient four‐step iterative process, designated as the DM scheme, for approximating fixed points of nonlinear operators within the framework of Banach spaces. We establish both weak and strong convergence results for the class of generalized ‐nonexpansive mappings. In addition to the convergence analysis, we investigate the stability and data dependence of the proposed algorithm to ensure its robustness under computational perturbations. The practical utility of the DM method is demonstrated through numerical applications in signal processing, specifically in the reconstruction of noisy signals through a fixed‐point formulation. Performance is analyzed based on error decay and signal‐to‐noise ratio (SNR) improvements. Furthermore, the applicability of the proposed method is illustrated through Caputo‐type nonlinear fractional differential equations subject to specific boundary conditions.
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