Axioms (Sep 2022)

Solving Fractional Volterra–Fredholm Integro-Differential Equations via <i>A</i>** Iteration Method

  • Austine Efut Ofem,
  • Aftab Hussain,
  • Oboyi Joseph,
  • Mfon Okon Udo,
  • Umar Ishtiaq,
  • Hamed Al Sulami,
  • Chukwuka Fernando Chikwe

DOI
https://doi.org/10.3390/axioms11090470
Journal volume & issue
Vol. 11, no. 9
p. 470

Abstract

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In this article, we develop a faster iteration method, called the A∗∗ iteration method, for approximating the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. We establish some weak and strong convergence results of the A∗∗ iteration method for fixed points of generalized α-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w2-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra–Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature.

Keywords