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Riemann–Liouville calculus on quadratic fractal interpolation function with variable scaling factors

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Abstract

In this paper, we explore the Riemann–Liouvllie fractional calculus of quadratic fractal interpolation function (QFIF) with variable scaling factors. Fractional calculus of QFIF with predefined initial condition is investigated in an arbitrary closed interval of \(\mathbb {R}\). Further, the relation between the order of fractional integral (derivative) and the box dimension of QFIF is established.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    A. Gowrisankar

  2. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, India

    M. Guru Prem Prasad

Authors
  1. A. Gowrisankar
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  2. M. Guru Prem Prasad
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Correspondence to A. Gowrisankar.

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The authors have declared that no conflict of interest exists.

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The research does not involve any human participants or animals. Therefore, we do not need the statement on welfare of human participants or animals.

Additional information

The research work has been supported by Indian Institute of Technology Guwahati, India under the scheme of Institute Post Doctoral Fellowship, Ref: IITG/ACAD/408/2016-17/69.

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Gowrisankar, A., Prasad, M.G.P. Riemann–Liouville calculus on quadratic fractal interpolation function with variable scaling factors. J Anal 27, 347–363 (2019). https://doi.org/10.1007/s41478-018-0133-2

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  • DOI: https://doi.org/10.1007/s41478-018-0133-2

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