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A numerical method for solvability of some non-linear functional integral equations

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  • Deep, Amar
  • Deepmala,
  • Rabbani, Mohsen

Abstract

In this article, we prove the existence of solution for some non-linear functional integral equations of two variables in Banach algebra C([0,b][0,c],R),b,c>0, which is the generalized the results of several papers. We use the idea of Darbo fixed point theorem for the product of operators in the above space. Modified homotopy perturbation method to solve these types of non-linear functional integral equations is also explained with a supporting example.

Suggested Citation

  • Deep, Amar & Deepmala, & Rabbani, Mohsen, 2021. "A numerical method for solvability of some non-linear functional integral equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300320305919
    DOI: 10.1016/j.amc.2020.125637
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    References listed on IDEAS

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    1. Biazar, J. & Ghazvini, H., 2009. "He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 770-777.
    2. Biazar, J. & Ghazvini, H. & Eslami, M., 2009. "He’s homotopy perturbation method for systems of integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1253-1258.
    3. Yanying Ma & Jin Huang & Hu Li, 2015. "A Novel Numerical Method of Two-Dimensional Fredholm Integral Equations of the Second Kind," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, July.
    4. Biazar, J. & Eslami, M. & Aminikhah, H., 2009. "Application of homotopy perturbation method for systems of Volterra integral equations of the first kind," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3020-3026.
    5. Rabbani, Mohsen & Arab, Reza & Hazarika, Bipan, 2019. "Solvability of nonlinear quadratic integral equation by using simulation type condensing operator and measure of noncompactness," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 102-117.
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    Citations

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    Cited by:

    1. Kazemi, M. & Yaghoobnia, A.R., 2022. "Application of fixed point theorem to solvability of functional stochastic integral equations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    2. Deep, Amar & Deepmala, & Hazarika, Bipan, 2021. "An existence result for Hadamard type two dimensional fractional functional integral equations via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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