Abstract
In this paper, a new idea of exploring the variable order fractional calculus on the fractal interpolation functions is addressed. The studies of constant order fractional calculus on the fractal functions are generalized to the case of variable order. The Riemann–Liouville variable order fractional integral (/derivative) and the Weyl–Marchaud variable order fractional derivative are investigated over the different kinds of fractal interpolation functions (FIFs). Furthermore, the necessary conditions of variable fractional order p(z) defined on the interval $$[x_0,x_N]$$ are also derived. It is observed that under the derived conditions, both the Riemann–Liouville variable order fractional integral (/derivative) and the Weyl–Marchaud variable order fractional derivative of FIFs are again FIFs interpolating new data set.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
