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On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order

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  • Mishra, Lakshmi Narayan
  • Sen, Mausumi

Abstract

In this paper, we present some results on existence of solutions for a quadratic Volterra integral equation of fractional order in two independent variables. This equation is considered in the Banach space of real functions, defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive. An example is provided to illustrate the theory.

Suggested Citation

  • Mishra, Lakshmi Narayan & Sen, Mausumi, 2016. "On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 174-183.
    • Handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:174-183
    DOI: 10.1016/j.amc.2016.03.002
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    Cited by:

    1. Vijai Kumar Pathak & Lakshmi Narayan Mishra, 2022. "Application of Fixed Point Theorem to Solvability for Non-Linear Fractional Hadamard Functional Integral Equations," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    2. Minjibir, M.S. & Mohammed, I., 2018. "Iterative algorithms for solutions of Hammerstein integral inclusions," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 389-399.
    3. Sen, Mausumi & Saha, Dipankar & Agarwal, R.P., 2019. "A Darbo fixed point theory approach towards the existence of a functional integral equation in a Banach algebra," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 111-118.
    4. Li, Pingrun, 2017. "Generalized convolution-type singular integral equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 314-323.

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