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An efficient method for solving neutrosophic Fredholm integral equations of second kind

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Abstract

In this article, a numerical method for the solution of neutrosophic Fredholm integral equation has been investigated. In addition, the neutrosophic Fredholm integral equation has been presented in the sense of \((\alpha ,\beta ,\gamma )-\)cut using Riemann integration approach. Some basic properties of neutrosophic calculus such as neutrosophic integral, neutrosophic continuity have been introduced. An iterative method has been modified in neutrosophic environment to find the numerical solution of Fredholm integral equation of second kind. The convergence of the iterative method in neutrosophic environment has been demonstrated in terms of some theorems. In the iterative method, trapezoidal rule has been used to evaluate the integral and find the approximate solution of the equation. In addition, the convergence of the trapezoidal approximations has been provided in terms of theorem. The algorithm of the proposed method has been given in the numerical method section, which briefly helps to understand the proposed method. A comparison of our method with other existing methods has been discussed to show the efficiency and reliability of our proposed method. In addition, a brief discussion about the advantages and limitations of our method has been provided. Some numerical examples have been examined to show the validation and effectiveness of the proposed method. In addition, different types of error analysis have been investigated by providing different types of tables and figures.

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Acknowledgements

In this work, the study of Sandip Moi is funded by Council of Scientific and Industrial Research (CSIR), Government of India (File No.- 08/003(0135)/2019-EMR-I).

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Authors and Affiliations

  1. Mathematics Discipline, School of Sciences, Indira Gandhi National Open University, New Delhi, 110068, India

    Suvankar Biswas

  2. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, B. Garden, Howrah, 711103, India

    Sandip Moi & Smita Pal Sarkar

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  1. Sandip Moi
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  2. Suvankar Biswas
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  3. Smita Pal Sarkar
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Correspondence to Suvankar Biswas.

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Moi, S., Biswas, S. & Sarkar, S.P. An efficient method for solving neutrosophic Fredholm integral equations of second kind. Granul. Comput. 8, 1–22 (2023). https://doi.org/10.1007/s41066-021-00310-1

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  • DOI: https://doi.org/10.1007/s41066-021-00310-1

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