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Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models

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  • Jingwen Zhang

Abstract

In this paper, we present and demonstrate an innovative numerical method, which makes use of fuzzy numbers and fuzzy parameters that is effective in the solution of fuzzy type Volterra integro‐differential equations, which was previously thought to be impossible using conventional methods. The first application of a technique for solving Volterra integro‐differential equations of the fuzzy type, which was devised and tested in this paper, is shown here. This is the first time that this approach has been used. This system’s overall quality may be improved as a consequence of the use of the Hilbert space replicating kernel idea, which is a possibility. Separate evaluations are made of the algorithms’ correctness and sloppiness, as well as their foundations in the computationally effective kernel Hilbert space, which has been extensively researched in the past. Numerical examples are provided of the article to demonstrate how the technique outlined before may achieve convergence and accuracy. Here are a few illustrations to help understand that it is possible to deal with physical issues that require complicated geometric calculations with the assistance of the method explained in this article.

Suggested Citation

  • Jingwen Zhang, 2022. "Convergence Analysis Hilbert Space Approach for Fuzzy Integro‐Differential Models," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3991262
    DOI: 10.1155/2022/3991262
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    1. Tingting Cai & Dongmin Yu & Huanan Liu & Fengkai Gao, 2022. "RETRACTED: Computational Analysis of Variational Inequalities Using Mean Extra-Gradient Approach," Mathematics, MDPI, vol. 10(13), pages 1-14, July.
    2. Fengyun Zhang & Funing Lin & Guangwang Su & Guangming Xue & Ahmed Mostafa Khalil, 2021. "Decay Estimates for a Type of Fuzzy Viscoelastic Integro-Differential Model," Complexity, Hindawi, vol. 2021, pages 1-19, March.
    3. Al-Smadi, Mohammed & Arqub, Omar Abu & Shawagfeh, Nabil & Momani, Shaher, 2016. "Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 137-148.
    4. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
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