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Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order

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  • Ming Li
  • Wei Zhao

Abstract

This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.

Suggested Citation

  • Ming Li & Wei Zhao, 2013. "Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-4, May.
    • Handle: RePEc:hin:jnlamp:806984
    DOI: 10.1155/2013/806984
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    Cited by:

    1. Chenkuan Li & Kyle Clarkson, 2018. "Babenko’s Approach to Abel’s Integral Equations," Mathematics, MDPI, vol. 6(3), pages 1-15, March.

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