@article{Filali2025, 
author = {Doaa Filali and Mohammad Akram and Mohammad Dilshad},
title = {Exploring the fractional Volterra-Fredholm integro-differential equation: An iterative approach},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {23467-23495},
keywords = {contractive-like mapping, Gα-RSNEM, fixed point, ω2-stability, nonlinear fractional Volterra-Fredholm integro-differential equation},
url = {https://www.sciopen.com/article/10.3934/math.20251042},
doi = {10.3934/math.20251042},
abstract = {In this paper, we construct a new four-step iterative method and show that our newly designed scheme converges faster than a number of iterative methods. We corroborate our claims by performing numerical experiments. We analyze the strong convergence result to approximate the fixed point of a contractive-like mapping and establish the weak        ω          2      -stability of our scheme. Further, strong and weak convergence results are incorporated for a generalized    α-Reich-Suzuki nonexpansive mapping under some mild assumptions. We also illustrate numerical examples to validate our theoretical claims. Finally, we set forth our scheme to explore a Caputo-type nonlinear fractional Volterra-Fredholm integro-differential equation and a fractional diffusion equation.}
}