Riemann–Liouville fractional integral of non-affine fractal interpolation function and its fractional operator
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, 632 014, Vellore, Tamil Nadu, India
Accepted: 25 October 2021
Published online: 7 November 2021
This paper mainly investigates the Riemann–Liouville fractional integral of -fractal function and fractional operator of -fractal function that maps the given continuous function to its Riemann–Liouville fractional integral. The Riemann–Liouville fractional integral is explored for -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 -fractal function are investigated. Finally, the semigroup property for the collection of fractional operators defined on are discussed.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021