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Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution

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  • Hazarika, Bipan
  • Srivastava, H.M.
  • Arab, Reza
  • Rabbani, Mohsen

Abstract

The aim of this article is to investigate the existence of solution for the nonlinear functional integral equations with the help of measure of noncompactness, simulation function and generalized Darbo fixed point theorem. Also we provided example for the applicability of obtained results to the theory of integral equations. Also we introduce an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to find solution of the above problem with high accuracy. Finally we have a discussion about convergence and upper bound of error.

Suggested Citation

  • Hazarika, Bipan & Srivastava, H.M. & Arab, Reza & Rabbani, Mohsen, 2019. "Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 131-146.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:131-146
    DOI: 10.1016/j.amc.2019.04.058
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    References listed on IDEAS

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    1. H. M. Srivastava & Sachin V. Bedre & S. M. Khairnar & B. S. Desale, 2014. "Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, August.
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    Cited by:

    1. Panda, Sumati Kumari & Ravichandran, C. & Hazarika, Bipan, 2021. "Results on system of Atangana–Baleanu fractional order Willis aneurysm and nonlinear singularly perturbed boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Rabbani, Mohsen & Das, Anupam & Hazarika, Bipan & Arab, Reza, 2020. "Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Deep, Amar & Deepmala, & Ezzati, R., 2021. "Application of Petryshyn’s fixed point theorem to solvability for functional integral equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    4. 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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