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Riemann–Liouville fractional integral of non-affine fractal interpolation function and its fractional operator

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Abstract

This paper mainly investigates the Riemann–Liouville fractional integral of \(\alpha \)-fractal function and fractional operator of \(\alpha \)-fractal function that maps the given continuous function to its Riemann–Liouville fractional integral. The Riemann–Liouville fractional integral is explored for \(\alpha \)-fractal function by choosing vertical scaling factor as a constant as well as a continuous function defined on the closed interval of interpolation. Further, the boundedness and linearity of the fractional operator of \(\alpha \)-fractal function are investigated. Finally, the semigroup property for the collection of fractional operators defined on \({\mathcal {C}}(I)\) are discussed.

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Acknowledgements

The authors are grateful to Dr. M.A. Navascués, Departamento de Matemática Aplicada, Universidad de Zaragoza, Spain for spending valuable time on the constructive evaluation of the paper and sharing her suggestions towards the improvement of the paper.

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Priyanka, T.M.C., Gowrisankar, A. Riemann–Liouville fractional integral of non-affine fractal interpolation function and its fractional operator. Eur. Phys. J. Spec. Top. 230, 3789–3805 (2021). https://doi.org/10.1140/epjs/s11734-021-00315-6

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00315-6

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